Ashnod's alter and the stack. (aka JUDGE!)

[Vastros]

Say your opponent controls ashnods alter and one llanowar elf. You have 2 tundra untapped. You vapor snag the elf, in response they sacrifice it to the alter, in response you StP the elf, can they re-sacrifice the elf the the alter in response?

[Koby]

Say your opponent controls ashnods alter and one llanowar elf. You have 2 tundra untapped. You vapor snag the elf, in response they sacrifice it to the alter, in response you StP the elf, can they re-sacrifice the elf the the alter in response?

'Sacrifice' is a specific game-play meaning that immediately puts the card into the graveyard. For Ashnod's Altar, sacrifice is part of the ability's cost. Costs (both mana and others) cannot be responded to, and are paid for during the announcement/targeting (if applicable) of the ability.

In the specific example, the play would happen like this:

You: Swords to Plowshares, targeting Llanowar Elf (paying :w:)
Opp: In response, activate Ashnod's Altar and sacrifice the Llanowar Elf (payment: sacrifice)

The stack would now look like this (top to bottom):
* Ashnod's Altar (Add :2: mana) - Special note: mana abilities do not use the stack whatsoever.
* Swords to Plowshares (Exile Llanowar Elf)

Remember that any action that occurs before the semi-colon ( : ) is considered a cost and must be paid before the ability goes onto the Stack.

[Kich867]

Say your opponent controls ashnods alter and one llanowar elf. You have 2 tundra untapped. You vapor snag the elf, in response they sacrifice it to the alter, in response you StP the elf, can they re-sacrifice the elf the the alter in response?

To clarify the above answer:

1) You vapor snag the elf, it goes onto the stack.
2) They sacrifice the elf to ashnod's altar.
3) You STP the elf in response.
4) They sacrifice the elf to ashnod's altar again..?

So the real answer here is in 2. At point 2, Ashnod's Altar doesn't read: "0: Sacrifice a creature and add 2 mana to your mana pool." It reads: "Sacrifice a creature: Add 2 mana to your mana pool". Sacrificing a creature is a cost to Ashnod's Altar. You cannot respond to costs, it just happens. You can respond to "Add 2 mana to your mana pool", not "Sacrifice a creature".

Just like he can't respond to you tapping your blue mana source, you can't respond to him sacrificing the elf. Your STP in step 3 has no valid target because the elf is already dead.

[Koby]

Good point Kich, I missed that important aspect about being unable to cast StP on the Elf; since it is no longer there.

(Alas! I am only human! :)