From the conjure elemental spell description (PHB, pg. 225):
The elemental disappears when it drops to 0 hit points or when the spell ends.
Can I rip parts off of an elemental before it disappears?
Role-playing Games Stack Exchange is a question and answer site for gamemasters and players of tabletop, paper-and-pencil role-playing games. It only takes a minute to sign up.
Sign up to join this communityFrom the conjure elemental spell description (PHB, pg. 225):
The elemental disappears when it drops to 0 hit points or when the spell ends.
Can I rip parts off of an elemental before it disappears?
As the part you quoted from the PHB says:
The elemental disappears when it drops to 0 hit points or when the spell ends.
All parts of the creature will go with it when it disappears.
There are no specific rules that state this. However this is how all DM's I know would rule this. Were the spell a summoning spell and stated that the creature "returns to its plane" at the end I would rule differently.
The books don't go into detail about harvesting bodyparts from monsters. Occasionally a monster will note that its venom can be extracted, but 99% of the time, the Monster Manual does not go into detail about this kind of ordeal.
This is a game about epic dungeon crawling, not about being a Monster Hunter who gathers bodyparts, so the game is pretty much silent on the matter. It even extends to humanoid enemies, who should realistically drop the things they are wielding, which the Monster Manual suggests not doing to avoid giving too much loot to the players.
So in other words.... regardless of if bodyparts taken from the elemental disappear or not once it dies, which would be something to ask your DM (I'd personally say that the elemental, its bodyparts and everything it was wielding disappears), the entire ordeal of harvesting bodyparts from a monster is something entirely in the DM homebrew realm.
Ask your DM and see what they say.