Cut a piece of copper mesh with scissors to the size of the hole you wish to fill. Coat the copper mesh thoroughly with a quick-drying interior or exterior patching compound.
Stuff the copper mesh tightly into the hole.
Apply additional patching compound to the hole with a putty knife. Scrape off the excess compound once the hole is full. Allow the patching compound to dry for the length of time specified by the manufacturer. Apply a second layer of patching compound if necessary. Once the final layer of patching compound is dry, sand the patched area until it is smooth and paint over it if desired.
Measure the hole. Add 2 inches to the width and length.
Put on work gloves. Cut a piece of hardware cloth with tin snips to the size you calculated in Step 1.
Center the hardware cloth over the hole and fasten it securely with fencing staples. Position the staples close together so that mice and other rodents can’t gnaw or push between them. Fill the hole with patching compound or foam caulk.