My Yucca has been in the same spot for over 40 years. Every-so-often, I prune it, but have let it go for several years. The roots seem to go down well over a foot, and the root balls have grown up and are inches thick with small shoots on every side. I used to always remove the part of the plant that had bloomed, but have not, again for several years. Today, I took a pickup truck load of plants, dead leaves and root balls out of the bed. I would estimate at least half of the whole. Can I actually cut these root balls down the ground? Plants started with a single plant about 46 years ago. Now is about 5 x 10 feet, and who knows how deep it goes.
If your trying to remove the Yucca entirely you will need to remove all of the roots. Any part of the root left in the ground will grow another plant.
Here are some links for you with more information.