i agree, a true cutting from the base might not root well. but if you dig down a bit and get a good chunk of the main roots, it should root fine.
if it were me i would dig about 2-3 feet on either side of that base and go down as far as you can, say at least 3 feet. then use a saw and cut the roots trying to keep as many as you can intact.
once cut and puller out, let the roots dry in open air for week or 3

after that replant with really good support.
how you are going to pull such a massive cactus, i am nut sure. a crane, or even pulleys and a good frame will help but be pricey. maybe you can hire a landscaping company or someone with a small crane to pull it out when you cut and lay it down (carefully) when your done? then again later on when you want to plant it?
no matter what it is not going to be easy, and will probably cost some $.
Stephen Robert Irwin: 22 February 1962 – 4 September 2006. Rest In Peace.