You might have squirrels instead of mice. One of those traps can rap a squirrel right in the head and it will only daze them. Then they'll just take the food. I had both problems actually when I moved into my current house. Squirrels and real mice both.

The mice I took care of with the old school Victor traps. I oiled the springs and any metal-to-metal contact surfaces with vegetable oil. This made them extra powerful and fast. Then I proceeded to bend the metal tabs on the triggers so that they would barely hold the spring-loaded arm in place. In other words I made a hair trigger. I oiled that part too when I was finished. Careful handling a loaded trap like this, they are very touchy. Finally, I used processed american cheese slices as the bait. They absolutely love the stuff, and it has just the right consistency that they can't lick it off (like peanut butter), but it's still squishy enough to cram it under the crevices of the trigger so it can't simply be lifted off without triggering. I think I only had one fail after I did all this and I think it may have been a lucky one that had kicked some debris onto the trigger. Also, change your baits frequently. They like fresh food.

After I figured out how to trap them out, I went around the house and found all points of potential ingress and sealed them up. There were several soffit vents and baseboard vents with screens in them that the screens had rusted out and been destroyed. I replaced all of those, and plugged up a couple holes that had been cut or drilled in the siding over the years, along with a crawl space entry door that was damaged and had a huge gap in it. A few days after finishing this I stopped finding mice in my traps. I do occasionally still trap mice in the garage, but it's because they come in and out while I'm working in there or outside, so I can't really stop that. I just keep traps in place for when they do so they don't make it deeper into the house.

The squirrels were relatively easy to trap if you have those getting in the house. I bought a live trap called the Squirrelinator at the advice of my neighbor. You need to put this on a flat hard surface outside that they can't dig under like a wooden deck or a concrete slab, and put a piece of plywood on the top with rocks or concrete blocks to hold it down. Otherwise they'll dig under or reach in from the top and take your bait. They love the pre-packaged bird feed found at pet stores that consists mostly of ground feed corn. They also like cheap white bread with refined flour in it, not the fancy whole grain stuff. I would just put it on a little paper plate away from the edges and the entry door so they had to go all the way in to get it. I trapped one every day for weeks with that setup. We were overrun with them.