[Andrew Hackard]

First, you were wrong: Mate copies a monster, but it is itself a distinct monster that must also be defeated. Making one go away doesn't affect the other (which is why we advise discarding the Mate card for simplicity).

That said, your opponent's play was legal. He's allowed to use any resources at hand during the fight or Run Away phase, even if those resources were promised to someone else. Yes, it sucks that he did that, but it was a legal play and probably a smart one, too.