Dig to loosen the soil 6 inches in a 1- to 2-foot diameter around the base of the cactus.
Wedge your shovel underneath the cactus plant. Wedge it deep enough to sever the long taproot that runs from the center of the plant's root ball. If the cactus is short and squat, then try pushing down on the handle to lift the cactus up and out of the hole. If it is very tall, push it over, instead of lifting it out. Apply pressure with your shovel near the top of the cactus to push it away from you. If the shovel won't move the cactus, you'll have to pull it out of the hole. Tie a rope around the cactus, stand back and pull it over or out of the hole. If the cactus is very heavy, enlist a buddy or two to help.
Haul the cactus away. Lift it into a wheelbarrow, drag it away by the rope or cut it into pieces and bag it on the spot. Remove all of the cacti material from the area; large sections may root on the spot.