Well, part of the problem is that when we talk about death, there are multiple definitions.
Medically, you have "clinical death" and "brain death." There is also the definition of death which means "the end of life." The latter is even more of a problem because where most people consider "life" to mean a certain level of functioning, science defines life based on more than organ functions. Starting at a very young age, in schools, we are often taught that the basic way that science defines life is that life is something that can:
- Reproduce
- Grow
- Move
- Have a metabolism (obtain and use
energy)
So, starting with brain death, yes, it is possible for the brain to cease functioning almost instantly. While we don't have many details on what the experience is like when the brain is shutting down, we do have studies on the activity in the brain afterward. It is most likely the case that during death, the brain will send signals based on external stimuli, as that is its main function, and because those stimuli are extreme, the brain's activity will probably also be pretty high. Because instant injuries, such as the one mentioned, create irreversible damage to parts of the brain that send and receive signals, instant brain death is possible because it would be much like ripping conductive wires apart that support a larger, electrically-driven apparatus, the parts of the brain affected by the injury would instantly turn off.
Clinical death is a little bit different and is vaguely defined. Generally, clinical death involves stopped breathing, but it can also involve cardiac arrest and the failure of various organs and biological systems. Clinical death is often not considered actual death because someone who is clinically dead can sometimes be revived. So, while someone may suffer injuries that causes clinical death to be sudden, because the brain hasn't necessarily shut down in the event of clinical death, they may actually experience something while they're unconscious and dying. This is what scientists think is responsible for near death experiences which many claim are related to the afterlife. Instead, though, these reports of near death experiences are likely similar to lucid dreams, in which it is difficult to differentiate between what is happening in one's head while sleeping and what is actually happening while awake.
Approaching the question of death as the end of life, as defined by science, is a whole different realm than defining brain death and clinical death. For at least a short time after we die, cellular processes can sometimes continue, even when the heart has stopped, breathing has stopped and the brain no longer is functioning. The cells function as long as their basic structures are in tact and the nutrients they are surviving on are still available. Thus, some of an individual's metabolic processes, like storing fat, will continue to happen for over an hour (probably more) after the brain, lungs and heart have completely shut down. Reproductive cells will function for a while after death and the process of death, itself, will cause an individual to move, sometimes. Because of this, a corpse still satisfies the definition for life that we're often given in grade school science classes. If consider death at this level, the only way instant death could occur is if the cellular structures of the body, including our symbiotic microbes, were instantly destroyed.
When people refer to "instant death," though, in the sense that you describe, they're usually talking about what level of awareness someone has as they're dying. Did they feel pain for some time or did they experience some emotional state as they passed away? In that sense, instant death is not uncommon. Certain types of brain injuries do damage the brain to the point that it can no longer send signals related to processing stimuli. Decapitation may be another matter, though, because the brain may be severed from the body, but it can still send signals for a very short time. There are, in fact, anecdotes about decapitated heads responding to stimuli after being separated from their body (not that anecdotes are great evidence, but that's what we have. I know of no brain scan done on a decapitated head right after it was severed from the body).
There's no technical definition for "instant death." Instead, that is a term used in everyday jargon and not in the medico-science community as some official term. Death is too complex for that, as you can see.
