Bwahahahahaha. Pulling a chain around is how you SPREAD cactus, not kill it. Every little piece of cactus that touches the ground will grow into a new plant.
The normal cactus we get is prickly pear. If you have a lot of it, you might be ahead to burn the spines off of it and allow the cattle to eat it down to the ground.
Or you could refrain from any care in that field at all. After a couple years of undergrowth, there will come the cochineal bug. It looks like white pieces of cotton. Once you have the cochineal, they will wipe out the prickly pear for you. But they must have some undergrowth (duff) to survive. If you smash the white fluff, you will have red stain on your hands.
Here is a picture of cochineal infesting a prickly pear.