Go to the main electrical panel located in the garage, laundry room/mud room, or basement. Find the breaker powering the microwave and switch it off.
Go to the wall-mounted microwave oven and unplug the power cord from the electrical outlet. Wrap the power cord up, then wrap duct tape around the cord to prevent it from dangling or catching on something as you dismount the appliance.
Spread a drop cloth over a table or on the countertop. Open the microwave and pull out the cooking tray and/or grates from inside the appliance. Put the cooking tray and the grates onto the drop cloth.
Close the microwave door and tape it shut with duct tape to keep the door from accidentally popping open while you remove it from the wall.
Locate the mounting bracket underneath the appliance. Have someone hold the appliance while you unfasten the mounting screws going through the mounting bracket into the microwave with a screw gun.
Pull the microwave off the mounting bracket once it's free and place it onto the drop cloth, with the help of your friend or family member.
Unfasten the mounting bracket from the wall with the screw gun to finish.