Dig around the yucca plant starting one foot away from the base of the plant. Dig a circle around the plant until you find the roots.
Dig away the dirt from the roots of the yucca plant. Take care not to break the roots as you work.
Grasp the swordlike leaves of the yucca and pull upward from the ground. It should come away easily if you loosened and removed enough dirt from the roots. Set the yucca plant aside if you're transplanting or dispose of it if you're not keeping it.
Sort through the dirt with a pronged garden cultivator to find small pieces of root left over from the yucca plant. Discard the remnants.
Keep an eye on the spot. Even small pieces of yucca root can sprout in a few weeks or up to a year, according to the Ohio State University website. Pull out any yucca shoots that sprout, taking care to remove the roots as well.