I am sorry for this delayed reply to your gardening question. We are transitioning to a new Q&A system and your question was unfortunately lost in the transition. I have discovered it now and hope this reply is not too late to be of help.
The best option is to break it off and/or pull it over to remove sections at a time. Depending on what type of cactus this is you may be able to do so with a hoe or a chain/cable looped around it or even a shovel. If you can break the topgrowth off in sections then it will be easier to pick them up with a shovel to move them to a trash can. Then dig out the base. Make sure and pick up all the pieces as cactus has an uncanny ability to root and regrow from fallen pieces!
Thanks for the question. Please stop in again soon!
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