Unfortunately cuttings cannot be taken from Yuccas. They grow from one central point, however they may produce off shoots around the main stem which are under the soil level and from the main root system. These can be removed taking root with them and potted on to form another plant, alternatively they will grow around the main stem of your plant.

Just wait for the off shoots. My neighbor took one out, concreted over it, poured oil, sea water, and he still has it coming up. I cut down a Hawaiian woodrose, and it had wrapped itself around one of my Yuccas. When I pulled, the yucca fell over, broken. But not to worry, there were three small ones hiding, so I cut down two to give the other one room to grow. One tip: cut the tip (about 1/4 inch) off each leaf. It won't show and it won't poke you every time you walk near it.