I cast Cryptic command choosing the modes of "tap opponent's creatures and bounce a creature." If my opponent kills the creature I want to bounce in response, will cryptic still tap their team?
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And on that day, Garfield said unto the world "Go ye forth and durdle!"
No. Cryptic Command has 1 target in this case. As it goes to resolve, it will check to make sure that target is still legal. Since it is not, the entire spell is countered by the game rules. None of its effects happen.
It will not. In your scenario Cryptic Command only has one target and if that target is no longer legal at the time of resolution (it is already dead for example) then your Cryptic Command will be countered on resolution for having no legal targets.
Cryptic command resolution [SOLVED]