@PatrickoftheG If you can, grab it by the head with one hand, pull by the hind legs. This will severe the spinal cord and lead to a quick death. This is how my father killed his lab rodents. And yes, it would be great to live in a better world.
Right now we use live traps and release the mice near thick piles of branches, hoping some of them will survive. Or at least they'll feed our owls.