I don't know about that yucca but most have insanely deep root systems,if it is already meesing with the house it will need to be moved as you know.Can you replant it some where away from the house?You may be removing little yuccas for next couple years if you don't get all the roots-

yuccas are easy to root. Cut it off close to the base and let it dry out. Plant in a well draining soil, for a tall cutting you will need to stake it.
It will lose a lot of it's leaves but will start growing again next summer.
If you are in zone 7-10 you can do this now.
Shorter cuttings are easier but since you have such a nice large plant try to save as much stem as possible.
If it doesn't make it just cut it off and try again.
As the link sugguest you will need to use Roundup to kill the root. Do this while cut is fresh do not let it dry out first. I would soak the root with a very strong solution. Make holes in the root ball with a large nail or stake and fill it with Roundup.
Your yucca looks to be a Yucca aloifolia and is very beautiful. I hope you are able to save it.
Wrapping it in a very thick tarp will make it easier on the arms.
http://www.bennyskaktus.dk/Yucca_FAQ_UK.htm#too_tall_yucca

Here is a link that might be useful: rooting a yucca