I really hated dealing with mice, from the droppings in silverware drawers to having to deal with an injured mouse because the trap didn't work just right. Eventually I removed their desire to take up residence in my house, which meant that I cleaned my kitchen very thoroughly and removed all sources of food odor and kept it that way. A mouse can live a long time on what's under some oven-tops.This is an extreme case. If there is no other way out, then you have to kill. But if it is possible not to kill, then not to kill.
I've killed five mice thus far this winter; all quick kills thanks to the new and improved mouse trap I bought. Some feral cats walk our property line daily, and when I do get a mouse, I toss it onto their path. Someone always takes it.