As far as I am aware, these are the only things that result in death:
1. Separating all HEAD parts from the UPPERBODY, or destroying them.
2. Separating a LOWERBODY part from the UPPERBODY, or destroying them.
3. Destroying the UPPERBODY.
4. Physical injury or destruction of all THOUGHT parts, for creatures without NOTHOUGHT.
5. When the breathe counter reaches 0 (due to lung damage, drowning, or strangling).
6. When all blood is lost, destroyed (by temperature changes), or changed from its natural state of matter.
7. When the infection level reaches 100%.
8. Being crushed in a cave-in or drawbridge, frozen, or obsidianized.
Some unintuitive details:
"Destruction" of a part refers to cumulative trauma resulting in the part collapsing, bursting, or splitting, taking sufficient heat or cold damage, taking sufficient fire damage (which is different from heat damage), or changing its state of matter from its "natural" form (melting, boiling, condensing, or freezing). All tissues of a part must be destroyed for the part to be considered destroyed. If this is the cause of death, it will be indicated in the text that describes the creature's death. (Died in the heat, burned to death, died in the cold, frozen solid, melted, etc.)
Necrosis is buggy. I think it technically causes blood damage (which is why zombies aren't bothered by it) but the game will not recognize the creature as being dead until it gets into combat.
The more damage the lungs take, the more likely it is for the creature to be winded, but this will not kill them unless they are severely damaged or rendered non-functional through other means.
Damage to nerves destroys the functionality of body parts between the brain and the opposite side of those nerves. This is why injuries to the upper spine are fatal; they shut down the lungs which cause the creature to suffocate. Neck injuries to non-breathing creatures who still need brains (like vampires) are crippling, but non-lethal. Injury to the lower spine is not fatal, but it will render the legs non-functional.
The rules for THOUGHT parts are inconsistent. A single physical injury to the (last) brain will instantly kill the creature, but damage from other sources, like heat, cold, or necrotic syndromes, can do damage without triggering instant-kills, unless the part is completely destroyed. In these cases the brain will eventually stop sending signals to the lungs, causing the creature to suffocate, which is what actually kills them.
Hearts do not actually do anything and heart injuries are themselves harmless despite creating a flashing "Mortal Wound" indicator. However hearts also contain large arteries which cause heavy bleeding if cut.
Resurrecting creatures without giving them traits that let them survive their current state will ignore instant deaths, but they can still die from missing important parts (example: resurrect a headless corpse, and it will get up and then suffocate.) This only happens when modding, since all vanilla resurrections also make the creature breathless, bloodless, and able to function without a head. This is why you can have undead creatures without heads, but if you cut off the head of an undead creature who has one it will still die (because removal of the head is still an instant-kill even though it doesn't really need one.)