Mix 1 1/2 cups of chlorine bleach with 1 gallon of water. Pour this over all the mouse droppings to get them wet to prevent any particles from becoming airborne. Do this as soon as you spot the droppings, even if you're not yet prepared to clean them up.
Wear disposable rubber gloves that are free from holes. Pick up the droppings and put them in a plastic bag.
Wash the area where the droppings were located with the bleach water. Use paper towels or old rags.
Place the paper towels or rags and the rubber gloves in the plastic bag. Tie up or seal the bag and discard it in an outdoor trash can.
Wash your hands thoroughly with hot soapy water.