Dig it up and discard? Have someone else dig it up for you. Perhaps a local landscaper would be glad to take your cactus to use for his designs and would pay for it.

If you do it yourself, remember that you have to dig allllllllllll the way down through the root system and excavate, or it will come back.

If it's a Saguaro and you live in Arizona, you can't. It is
Illegal to harm them in any way.

If not, wear gloves and dig them out. Make sure you get
everything or they will keep coming back like weeds.

Run an ad on Craigslist for free cactus. Then tell them they have to dig it up.