Mice are rapid breeders and like to live in dark, comfortable places with adequate food and water supplies. They will typically come indoors from outside and make their homes in your attic, walls, basements or crawlspace. When you set out traps for the mice, specifically snap traps, some of the mice are smart enough to avoid being killed. But their legs or tails are injured and you can't pick them up safely to relocate them. In these instances, it is most humane to kill them quickly by drowning or crushing their skulls.
Fill the bucket with ice cold water.
Put on the heavy duty work gloves. This will protect your hands from bites and scratches and potentially transmittable diseases.
Pick up the mouse caught in the trap or drop the whole thing in the bucket if you cannot easily release the mouse.
Wait a few hours before checking on the mouse. If the mouse is floating on the water and not moving, it's dead. If it's moving even slightly, wait another hour.
Put the plastic bag on your hand inside out and pick up the dead mouse. Wrap the plastic bag around the carcass, tie it in a knot and drop it in an outside trash can.
Put on the heavy duty work gloves and place the mouse attached to the trap in the bottom of the empty bucket.
Use the large flat end of the baseball bat and hit the mouse in the head with it several times until it stops moving. If it's twitching, hit him again. Since a twitching mouse can still feel pain, make the death as quick as possible.
Detach the mouse from the trap and tie up the carcass in a plastic bag. Dispose of the carcass in an outside trash can.