Our cats keep mice out of the living areas of our house, but the cats don't go in the garage or the basement. I regularly set old fashioned mouse traps in both those places, baited with peanut butter. You have to keep checking them- also sometimes the mice manage to eat the PB without setting off the trap, so keeping the traps clean and baited is necessary. The traps kill mice regularly and they never get to multiply or settle in. 98% of the time it seems like the mice are killed instantly. I like the old traps much better than the idea of glue traps or poison, both of which i personally consider cruel ways to kill. Outside mice are not a problem for us.

Oakleaf- wow you have some persistent deer! You have my sympathies.