How do I permanently get rid of a yucca plant?

Drill a series of 1 to 2 inch (2.5-5 cm.) holes around the base. Pour stump remover or herbicide into the holes. This will spread throughout the root system and eventually kill it—at which time the yucca plant can be dug up and removed from the area.

What chemical kills yucca?

Spray the young yucca whorls as they appear with a suitable herbicide. Use an herbicide that contains glyphosate or triclopyr. Each little whorl only requires a small amount of herbicide applied in its center for effective treatment. Do not apply herbicide when weather is damp or the yucca is wet.