Miniature Schnauzers were bred to hunt vermin such as mice, rats, etc so it's truly in his blood to do so; however, be careful in case the mice may have ingested any poison and listen for any rabies notices in your area since either of these scenarios could cause serious harm to him.
It is in the dog's nature that he hunts the mice. I don't think there is harm in hunting the mice and eating them. But stop the dog doing it regularly. He might be habitual of that and may want to go out to hunt alone.