the best way is use a pair of gloves if there hostil mice (if you caught them with glue trap)
if they are store bought mice then they gennarly don't bite unless they feal thretend
get a towel, washcloth, or gloves and either hold its beak down or hold the beak from the side.
amputate the problem
train him/her and give it discipline
get a dog trainer also don't be rough or abusive to the animal
you must tell the dog no!! everytime he goes near them. if that doesn't work carry a squirt bottle with water ans squirt at him/her when they go nest them. Or you can get a pepsi can fill it with...