Yes, they can be killed, and also: yes, they can be captured and imprisoned, according to at least one ancient source (see next section).
Nothing in the original mythology states that the Titans are necessarily stronger than the gods. In fact, if anything, Hesiod's Theogony, for instance, repeatedly highlights the strength of the Olympians as an explanation of how they defeated their elder enemies to became the top dogs. Every situation bears different circumstances, which are what determine how easy or difficult it would be to capture or kill one of the gods. Not at all possess the same powers, resources or temperaments, so the results will vary on a case-by-case basis.
Ares' Greatest Misadventure
In Book 5 (Lines 381-391) of Homer's Iliad, the Oceanid Dione recounts the story to Aphrodite of how a pair of really young giant boys once wrapped the war-god Ares in chains and packed him into a metal jar, nearly killing him. (Further details on that in the second-last section below.) In this and every story in which a god is captured, his opponent is tremendously enormous, so I am assuming that the colossal size of the deity's captor is a major factor if not an outright requirement for the overpowering of the targeted divinity. Only two exceptions to this come to mind.
Hera's Tricky Golden Chair
In one of these exceptions, when Hephaistos [Hephaestus], the artisan of the gods, was young, he used a somewhat steampunk mechanical device—a golden chair with hidden fetters—to trap his mother Hera, who had thrown him away when he was a baby. Hera's other son Ares tried to release her from the trap but failed, whereupon none of the other gods could convince Hephaistos to extricate Hera from the device. Finally the wine-god Dionysos [Dionysus] tricked the artisan-god into getting drunk and brought him to Mt Olympos [Olympus] where Hera had been trapped, mother and son were conciliated to each other, and Hephaistos let Hera out of her inconvenient predicament.
Dionysos Goes on a Cruise
The other exception features Dionysos in his youth, wherein he is captured and bound in ropes by a band of Tyrrhenian pirates posing as operators of a passenger ship. Dionysos, however, is merely toying with these corsairs, whom he terrorises by transforming parts of their vessel into ivy and snakes before changing all these men into dolphins.
The Most Dead God Limited Edition
In Greek mythology there is only one instance of a full-fledged deity actually going through the full process of dying entirely as ordinary mortals do (although, in a way, he comes back to life again). This story, about Zagreus, however, is told by the Orphics, a mystical cult whose mythology was some distance left-field of the mainstream Olympian narratives and which borrows heavily from adapted Egyptian and Asian material. (More on Zagreus in the last section below.) Again there are two exceptions to this, which amount to not much at all after all.
The Tomb of Zeus
The first [exception] is a Cretan version of Zeus about whom it was said that he was actually a local prince who, like Adonis, had been gored to death by a wild boar. Several places on Crete Island displayed his tomb (one of which remains even down to the present day), but even in a time almost as far back as Homer and Hesiod, a famous poet and prophet named Epimenides, himself a Cretan, dismissed this story out of hand, decrying his fellow islanders as degenerate liars on account of this. A few centuries after Epimenides, Callimachus agreed with the Cretan prophet by quoting him on this point in his Hymn to Zeus. In between the times of these two, Pherecydes of Syros had expressed his belief that the Cretan Zeus tomb actually belonged instead to a giant who had been Zeus' school-teacher during the god's childhood on the island, and who thus was very closely associated with the Olympian king.
The So-Called Death of Pan
The second exception comes from an essay written by Plutarch c. 100AD, in which he narrates the tale of how an Egyptian sailor heard a voice announcing to him across the water that he should spread a rumour saying that "the great god Pan" had died. The deity in question never himself makes a cameo in the story, which to me is clearly a metaphor for the subject-matter of the essay, On the Obsolescence of Oracles. The news of Pan's death is an allegory of the decline of certain aspects of popular Ancient Greek religion in Plutarch's time.
Disambiguating and Dismembering Khronos and Kronos
There is a significant but often subtle and fairly confusing difference between the Titan Kronos (Κρόνος in Greek, which gets Anglicised to Cronos and Cronus), who became the father of Zeus; and the primordial mystical god Khronos (Χρόνος in Greek, which is Anglicised as Chronos or Chronus), the personification of time, who is essentially a part of the structure of the universe. In some Orphic cosmogonies Khronos is the father of Khaos [Chaos] and thus the ultimate origin of all things.
Even though Khronos, meaning "Time," from which we get English chronology, chronometer and chronicle, is a different word from Kronos, even in ancient times the two characters were confused and equated with each other. Plutarch mentions an allegorical interpretation that Kronos, who devours his own offspring, was a symbol of how the ravages of Time (Khronos) consumed posterity.
In the early 21st century AD, the most popular source for the idea that the Titan Kronos was chopped to pieces by his own children appears to be Rick Riordan's Percy Jackson and the Olympians series of books, movies and other related entertainment forms. Riordan does not seem to have invented this piece of neo-mythology, and from what I can tell it appears to have arisen from the conflation of the Titan with the Time-God.
In her 2012 poetry collection In the Fullness of Time, Anne Hughes' poem At the Sea's Edge says (p. 67):
Here is where death is—
time dissolved into that eternity
from which beauty is endlessly borne—
agony of Chronos dismembered;
joy of Aphrodite depth-born
There is a much older reference to the same mytheme, from 1862, in Volume 1 of the London Society Magazine. According to its article "On the Grotesque in Things Sorrowful" (p. 426),
Zeus... could only dismember his father Chronos or Time,
the author thus confirming that s\he thinks Zeus is the son of the primaeval time-deity.
Hughes, for her part, seems to be confusing the Titan (or perhaps the Time-God) with Kronos's father Ouranos [Uranus], the Sky. Kronos had dismembered Ouranos, not by chopping him to pieces, but by castration.
As early as the 19th century, therefore, the stories seem to have gotten heaped into a jumble in which Kronos and Khronos were totally merged, and the emasculation of Ouranos by Kronos somehow became the hatcheting of K(h)ronos by his child(ren) instead.
K(h)ronos Still in One Piece
There is, however, no ancient myth at all in which Kronos [the Titan father of Zeus] is chopped into pieces by anyone, whether by his own progeny or someone other. No such thing happens to the cosmic Time-God Khronos either, whether we equate him with the Titan or not. The worst thing that happened to Kronos the Titan is that he got imprisoned in Tartaros [Tartarus], the vast storm-pit at the lowest level of the Underworld.
But even while incarcerated therein he still received prayers and libations from his children on Mt Olympos, who, according to Iliad 14, were required to invoke his name and those of the other Titans in the Underworld in order to ratify their most sacred oaths. Some time after the Trojan War, Zeus released Kronos and the Titans from Tartaros and granted them amnesty.
Kronos, whose prison sentence had lasted thousands of years, was at this point still alive, well, and bodily intact. He ultimately, therefore, cannot be used as an example of a deity that died, except in the sense that he had inhabited the land of death for aeons, lying inert beneath the dwelling of the human dead who were housed in the layer of the netherworld which sat on top of Tartaros.
Ouranos, the character from whom originates the confused story about K(h)ronos being dismembered, himself did not die when his son Kronos chopped off a piece of him. It is he who was held down by his children and then dismembered. Of four of his sons, each one held down one of his four limbs, while a fifth son, Kronos, arose from the Earth beneath him in order to sever his reproductive organ from the rest of him.
Far from killing Ouranos, instead this action produced yet more life, for the blood which spilled from this violence impregnated the Earth, which from it gave birth to the Furies and the ash-tree nymphs, as well as, in some versions, the Giants. More famously yet, the severed genitalia, dumped by Kronos into the Sea, transformed there into the lascivious goddess Aphrodite.
Apart from the case of Zagreus, the loss of this one body-part is the most grievous injury sustained by any deity in Greek mythology. A very similar thing happens to Agdistis, a being born to Zeus and Gaia in Phrygia. Because Agdistis was born with both male and female organs, the gods feared the entity and cut off the male organ. Upon this emasculation, Agdistis was thenceforward the Phrygian goddess Kybele [Cybele].
An almond tree grew up out of Agdistis's discarded genitals. An almond from this tree then impregnated a local river-nymph, who gave birth to Attis, who, when he had grown up, was castrated and died. He was worshipped after his death and seems to have resurrected in his eunuch form. Attis evidently had been born and died a mortal man, only becoming a god after death, somewhat like Asklepios [Asclepius] and Herakles [Hercules].
The mutilation of Ouranos and Agdistis represents a reduction of their power rather than their destruction. Ouranos loses his rule over the universe and becomes a deactivated part of the cosmos like the more inanimate primordial deities such as Erebos [Erebus] and Tartaros. Meanwhile Agdistis now appears in a less threatening form to the other divinities.
Varied Forms of Injury and Incapacitation
There is otherwise no level of damage inflicted upon Greek deities which comes close to being as severe as any kind of amputation. For several thousands of years the crucified Titan Prometheus has his liver torn out but it grows back almost every day, and he seems to be bodily intact once this torture ends. In one battle against the super-strong mortal hero Herakles, Hades is wounded in the shoulder, Hera in her right breast, and Ares in the thigh. They are each badly hurt but after a visit to their doctor they are all good as new.
Typhon vs Zeus
Zeus has his head split open with an axe, a full-grown goddess bursts forth from his cloven skull, and he recovers just fine from that. Later in life Zeus undergoes an apparently more surgical procedure. As part of the Giants' attack on the Olympians, the cosmic-sized, many-armed, hundred-headed monster Typhon coiled around Zeus, presumably like a python with its prey, and cut the sinews out of Zeus's hands and feet. This apparently paralysed the king of the gods, whom Typhon then threw over his shoulders, carrying him across the Sea to his lair, a cave in Cilicia, Anatolia.
Here Typhon deposited Zeus, hiding the god's extraced sinews in a bear-skin which he placed under the guard of a female, part-dragon creature named Delphyne. Zeus's sons, the gods Hermes and Aigipan [Aegipan], managed to sneak past this sentinel and save their father by reconnecting him with his sinews. After this, a furious battle ensued between Zeus and Typhon which ended with the latter's demise or imprisonment.
At the onset of his attack Typhon had threatened to release the confined Titans from Tartaros, to distribute the goddesses—especially the virgins—as brides among the Titans, the Giants and himself, and to enslave the male deities. Because Heaven was too small to contain him, Typhon planned to tear it down and rebuild it, with himself as its overlord. Zeus, for his part specifically, was slated to became the western pillar of the Sky, replacing the Titan Atlas in this mode of imprisonment.
But once Typhon had Zeus in his mercy, for some reason never explained to us, he did not do anything to him worse than paralysing him. It seems that he could well have killed him, but perhaps Zeus was not so easily slain and Typhon just didn't now how to finish him off. Maybe he intended to first display him in a triumph after fulfilling his promise of unearthing the anciently defeated Titans.
Kidnapping the God of War
A somewhat comical scenario had transpired some time not too far removed from Typhon's attack. Poseidon, the King of the Sea, had consorted with his own granddaughter Iphimedeia, and she bore him a pair of gigantic twin sons named Otos [Otus] and Ephialtes. These kids, whose stepfather was named Aloeus, and after whom they were called the Aloadai [Aloads], grew by nine inches every month. By the time they were nine years old they were each nine cubits wide and nine fathoms tall. In more modern parlance, they were each 18 feet (roughly 6m) wide and 54 feet (approx. 16m) tall.
In circumstances regarding which we are not informed, the twins once kidnapped Ares, who thus went missing for thirteen months, during which no other deity, so it seems, knew where he was. Heriboia was the second wife of Aloeus, and she somehow found out that her husband's giant stepsons had Ares. She fed Hermes this bit of intelligence, and he came in stealth-mode to rescue Ares. The Aloadai had clapped Ares in "cruel bonds" and shoved him into a bronze urn, within which he almost died, perhaps mostly from muscular atrophy and starvation, before Hermes came and stole him out of there. Doing what these boys did to Ares must have required the imposition of a prodigiously incredible amount of brute strength.
I base this on the fact that in the same poem which gives us the twins' measurements we are told that Ares' body, when he fell down, covered seven plethra of land, which is something like 6.3 square kilometres (almost 4 square miles). This comes from Iliad 21.405-410, the measurements contained therein having been translated variously into English as "seven roods" (A.T. Murray, 1924), "seven acres" (R. Lattimore, 1951) and "over an acre" (A.S. Kline's PoetryInTranslation website), all of which are significantly smaller than 6km2 or 4 miles2 but the least of which is still hundreds of times bigger than the Aloadai are supposed to have been.
In comparison to Ares, they might as well have been a pair of ants! We could perhaps explain this away by assuming that Ares, like his cousins Otos and Ephialtes, continued to gradually expand over the years so that he would have been significantly smaller back when they had nabbed him some generations earlier. Or that he only grew so extensively large on battlefields during wartime, such as in Iliad 21, which takes place in the thick of combat during the Trojan War.
The God Whom the Titans Assassinated
One of the most bizarre stories in Greek myth takes place after Zeus rapes his own daughter Kore, who, renamed Persephone, becomes the queen of the Underworld by marrying Zeus' brother, her own uncle Hades. Before she gets married, she gives birth to Zeus's son Zagreus, a beautiful, and sort of monstrous, horned god. In her jealousy over the affection lavished upon this stepson of hers, Hera organises for a bunch of Titans to attack Zagreus, and they chop him to pieces using, as Nonnus calls it in his Dionysiaca, "an infernal knife". This weapon might be some sort of ceremonial instrument from the Underworld.
This and other features of the confrontation with the baby god surely must be connected with the Mystery rituals of the Orphics: features such as how the Titans are able to sneak up on Zagreus because they have painted their faces with chalk and beguiled him with a mirror; and also the way in which he wildly changes himself into various forms before finally being slaughtered while in the guise of a bull.
Being butchered into beef is the closest that a Greek god ever gets to being "reduced to a state of formlessness from which they are unable to return". The conception of such utter destruction does not seem to exist in the ancient myths. Every entity in the universe from the Sky down to the Earth and its mountains, islands, rivers, trees, animals and people, has an essence which continues to exist even after the body's disintegration. This essence is contained somewhere in the cosmos, e.g. most of the dead descend beneath the Earth's surface and are held in the house of Hades.
There are a few different accounts of what happens to the pieces of the slain Zagreus but the most central is his heart, which Zeus preserves. Centuries later, this organ, now powdered, he makes into a special drink for his lover Semele, who becomes the mother of Dionysos. Thus Zagreus becomes reincarnated as the raucous wine-god, a unique position in the mythology, as we have no other Greek deity who is a reincarnation.
Most of the remaining butchered Zagreus-beef supplies the Orphic myth about the creation of humankind. The same Titans who assassinated Zeus's son then devoured his flesh. In his rage over this,
Zeus used his lightning to reduce the murderers to ashes, from
which, after being mixed with earth and water, humankind then arose...
The Orphics used this version of the creation story to explain why
human beings are stuck in a wheel of death and rebirth (virtually
identical to the concept of saṃsāra in Hinduism and Buddhism) with
the human soul (Dionysos Zagreus) and body (the Titans) as separate
entities, the former trapped inside, or being devoured by, the latter.
~ From my Answer to another