Yes, you can save the creature in this situation by untapping it in response
Murderous Compulsion, like every other targetted spell or ability, checks whether its targets are legal both when you choose targets, as well as on resolution of the spell. If on resolution, the creature previously chosen as a target is now untapped, the target becomes illegal (and because there's only a single target involved, the spell gets countered by the game rules for not having any legal targets).
601.2c The player announces his or her choice of an appropriate player, object, or zone for each target the spell requires. (...)
608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. (...) Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed (...). The spell or ability is countered if all its targets, for every instance of the word “target,” are now illegal. (...)
As for the stack - you would have to cast Aim High in response to your opponent's spell. Because the stack resolves from the top (last in, first out), your spell will resolve before theirs, untapping your creature before it would be destroyed.
405.2. The stack keeps track of the order that spells and/or abilities were added to it. Each time an object is put on the stack, it’s put on top of all objects already there.
405.5. When all players pass in succession, the top (last-added) spell or ability on the stack resolves. If the stack is empty when all players pass, the current step or phase ends and the next begins.