We have a storage building in our back yard. It has a raised floor, so there is space under it for the occasional critter. Our male dachshund, Reuben will go on full alert. His nose can follow the trail, and he will circle the storage building until we lock him out of the back yard.
He disposed of them in an all natural organic way. Dogs have eaten mice for as long as dogs have existed.
If he continues to circle the building, I bait some traps and with technology and peanut butter, I can catch more mice than the dog. They have in the past gotten into my garage. That is when the real battle begins. A mouse or rat can cause thousands of dollars in damage in a day or two to a car.