Can a Vorpal weapon kill creatures with the regeneration special ability?
For example, can a Balor's Vorpal sword kill a Pit fiend?
If not, what happens to the HP of a creature that has lost its head?
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I'm going to give a somewhat expansive answer here, because I think the topic of vorpal swords needs one.
tl;dr - Decapitated is a different status effect than Dead in 3.5e, and D&D in general; consult the monster stat block for more info.
A Vorpal weapon does not explicitly kill anything; the wording is important. As per the text, "Upon a roll of natural 20 (followed by a successful roll to confirm the critical hit), the weapon severs the opponent’s head (if it has one) from its body."
That is all it does. As the text goes on to explain in some examples, there is a very common resulting effect: "Most other creatures, however, die when their heads are cut off."
Creatures without a head are implicitly defined as unaffected in the text; "Some creatures, such as many aberrations and all oozes, have no heads."
Some creatures do not die from losing their head(s), and if the text is read as RAW, by default do not take any effect, negative or positive, from losing their head(s): "Others, such as golems and undead creatures other than vampires, are not affected by the loss of their heads."
A few other unmentioned creatures do not die from a vorpal effect, or at least not immediately. One example is given below.
So, the vorpal weapon doesn't "kill", per se. It decapitates. Death is a possible side effect. It comes down to the individual creature statblocks and the effects therein. For example, hydras with multiple heads can survive at least one vorpal attack, by RAW: "A hydra can be killed either by severing all its heads or by slaying its body."
Edit: For a more specific answer, see Nepene Nep's post.
No, they regenerate.
If you cut off the head of a regenerating creature, they can heal it or reattach it.
Regenerating creatures can regrow lost portions of their bodies and can reattach severed limbs or body parts; details are in the creature’s descriptive text. Severed parts that are not reattached wither and die normally.
Pitfiends unfortunately do not note how long it takes to regenerate their heads. A similar creature, Chain Devils, takes 2d6x10 minutes. It's gonna take a while.
If you hit them with a silvered or holy weapon, they will die.
Even if a Pit fiend loses his head by a Balor's Vorpal sword, he will not die.
The Pit fiend does not lose HP at all.
Because a Balor's Vorpal sword can only give subdual damages to a Pit fiend.
The Pit fiend 's head can return to his body and resurrect immediately by using the greater teleport spell-like ability.