As long as no frog in your yard is poisonous I guess it would be OK. Eventually he probably will decimate the local population which resolves the issue.
Just a word of caution: since you live among other homes, some people use mouse poison. It doesn't instantly kill the mice but they become sluggish and are still able to move around, which makes it easy for your pup to catch and eat them. Then he will ingest that same poison and it can ill your dog. This goes for all urban dogs in back yards.
Last edited by wolfy dog; 07-21-2019 at 03:30 PM.