I agree with Eric. There are lots of bacteria in the gut and dead mice are likely to decompose rapidly, even if refrozen or refrigerated. I would use or discard within an hour or two, personally. E. coli, for example, can double in number in about 30 minutes...

A useful analogy might be if you shot a deer or caught a fish. You wouldn't want to leave them uncleaned very long, and certainly, you wouldn't want to freeze, defrost and then refreeze (and defrost) either one and eat it!!!