Hola stacey
The last problem cacti we had we chopped down and hacked it to death basically, my husband used gardening gloves x2 and oven gloves to prevent him from being stabbed

Another tip for rotting down plants is to drill a hole in the base and pour diesel in it, but I doubt that is a very "friendly" option these days! LOL
What about roundup but if you have chickens I would avoid using that, we used roundup up to the point where we got chickens
Or try horse manure on it after you have chopped down, this will rot it inside 6 months and then you can use as a fertiliser the following year, it will take some time to rot down so be patient

Starve it of everything it needs to survive like light and water, if you cover with 2 foot of manure you are on to a winner

Simone