Dogs will hunt mice and rats too. My dogs would go outside each night and we would hunt the rats that were stealing my fruit and veg. The rats came from next door's illegal chop shop.
I taught a mini poodle how to hunt mice at the pet shop. She had it down pat in 30 minutes. We had wild mice in the shop and they would eat the bird seed out the back. Each week we were meant to go through and clean up any seed but most of the time it wasn't done.
One day I was there and the dog groomer had brought her mini poodle in. The dog had never hunted before in its life and was a couch dog. I called the dog over and moved bags of seed. Mice went everywhere and the dog jumped back and was nervous and almost scared. I called the dog back over and said "what's that"? The dog's ears perked up and then more mice ran around. She backed off a bit so I called her back and pointed and said "what's that"? A couple more bags got moved and each time I said "get it, get it, go on". Half an hour later and the dog was waiting with anticipation every time I moved a bag of seed and she jumped on every mouse she saw. We got about 30 adult mice and dozens of pinkies (babies without hair) that day.
A couple of days later the groomer was back with her dog. The groomer lives on a farm property with horses and there are lots of mice and rats there. During the days that followed my training session, the dog had killed and brought over a dozen mice and 2 rats back to the house. The owner was pleased with the dead rodents but didn't like waking up to them on the floor by her feet.