Relocation of house mice is not recommended. They likely will move back to the place where they were removed.
Translocation of house mice is not recommended because is an exotic and invasive species.
Euthanize mice by carbon dioxide asphyxiation. Cervical dislocation also is acceptable. For mice caught on glueboards, use a sturdy rod or stick to deliver a sharp blow to the base of the skull.
House mice captured around residences often are double-wrapped in plastic and disposed of in household garbage. Check your state regulations regarding disposal of carcasses.