Can you sacrifice a permanent to pay a cost after that permanent has already been targeted by a spell that would destroy it?

A permanent that has been targeted by a spell is still on the battlefield until that spell resolves. Being the target of a spell does not remove the permanent from the game or change its legal status as a permanent you control. You can freely use it to pay costs in the meantime.

Costs are paid during the process of activating an ability or casting a spell (CR 601.2g, 602.2). At the moment you pay a sacrifice cost, what matters is that the permanent is on the battlefield and you control it — not what spells are currently targeting it (CR 700.4 defines 'sacrifice').

If you sacrifice the targeted permanent to pay a cost, the destroy spell will then have an illegal target when it tries to resolve. Under CR 608.2b, a spell or ability that has all its targets become illegal is countered on resolution — it simply does nothing.

Concrete example: Your opponent casts Murder targeting your Llanowar Elves. Before Murder resolves, you activate Phyrexian Tower's ability, sacrificing the Elves to add two black mana. When Murder later tries to resolve, its only target is gone — it's countered by game rules and has no effect.

This interaction is intentional and strategic: sacrificing a targeted creature to an altar or similar outlet both generates a benefit and blanks the removal spell, since the permanent leaving the battlefield makes the targeting spell fizzle (CR 608.2b).