This might help ..

Controling Yucca : Remedy and Vegatable Oil.

Interestingly I have never needed to control Yucca here ... but for others I understand it can be a big headache.

Good Day ...

rachel3,
Personally I have not had the pleasure of removing a yucca.
I do have one in the garden that needs to disappear. Over the last few years I've seen them removed successfully twice. Once by my brother who after many attempts of mowing them off, chemicals, fire, and shovel, won the battle with
"The Bigger Backhoe"
The other time, one of my customers has a garden by a pond and a muscrat burrowed in next to the yuccas, only about 8-10 inches down and ate the root. Killed 10 plants and they never grew back.Unfortunately she liked her yuccas.
You might check around and see if you can find a muscrat.
I haven't been able to locate one. The rental place has all
kinds of bigger backhoes. Watch out for gas lines water lines and electrical/cable lines when you dig