Turn off the circuit breaker to the Kenmore garbage disposal. Once you turn off the circuit breaker, open the sink cabinet and remove the contents from the cabinet so you have full access to the disposal.
Remove the screw on the bottom of the disposal that secures the electric access panel door with a Phillips screwdriver. Remove the door. Insert the leads of a circuit tester into the wire nuts connecting the house wires to the disposal wires to ensure the power is off to the unit. Once you verify power is off, untwist the wire caps and separate the wires.
Loosen the screw securing the strain relief clamp to the metal wire conduit on the side of the Kenmore disposal with a Phillips screwdriver. Pull the conduit away from the disposal, bringing the house wires out of the unit. Twist the wire caps over the end of each individual house wire until you are ready to install a new disposal unit.
Place a bucket under the Kenmore disposal. Loosen the clamp screw securing the dishwasher drain hose to the side of the Kenmore disposal, if you have a dishwasher. Pull the drain hose from the disposal and set the end of the hose inside the bucket.
Turn the nut securing the disposal drain pipe to the sink S-trap counterclockwise with a pair of slip-joint pliers. Loosen the nut on the other end of the S-trap with the pliers, and swing the S-trap away from the disposal.
Insert a flat-head screwdriver into the side of one of the three locking lugs on the disposal mounting ring. Twist the screwdriver handle counterclockwise until the mounting ring unlocks. Grasp the Kenmore disposal with both hands, and turn it counterclockwise until it releases from the mounting ring.
Remove the three bolts securing the mounting ring assembly to the bottom of the sink drain with the Phillips screwdriver. Pull the mounting ring assembly away from the sink. Tap the bottom of the sink drain ring with a mallet until it is loose enough to pull out from the top of the sink.