The yucca plant is found in the desert regions across North America, and can flourish rapidly and aggressively even if not taken care. Some gardeners find this a blessing; others find it a curse. Getting rid of yucca plants is a tricky process, since you can't just cut it down to kill it--this may actually encourage several other yuccas to sprout up. The most effective way to kill yucca plants is to completely get rid of roots and plant parts through concentrated herbicide.
Cut down as much of the yucca plant as possible. Start by cutting off the side growth and branches with pruning shears or a hand saw until just the main trunk is left. Use an axe or chainsaw to cut down a very thick trunk, or pruning shears if it isn't much larger then the branches.
Paint the yucca tree trunk with tree stump remover (available at hardware stores or nurseries), covering every area of the plant that is exposed.
Drill a circle of 2-inch deep holes about 4 inches apart around the trunk's base, angling them down at 45-degrees. Pour the stump remover herbicide into each of these holes. This will ensure that the herbicide is circulated through the yucca's root system, effectively killing all of it underneath the ground.
Keep an eye on the yucca plant, as it will take a few weeks for the herbicide to completely kill it.
Kill any shoots that pop up out of the ground, which can be caused by pieces of roots that weren't entirely killed. Once the shoots are about 1 foot long, mix two parts diesel fuel with eight parts herbicide in a bucket and drench each shoot with this solution every day until they die off.