Certified GKH Gardening Expert
I would not cut it all off. You can trim back to the lower set of growths, but I wouldn't go any lower than that, since it is that far, established.
You may want to sterilize the chainsaw, beforehand. Making cuts that large can result in an infection, which can kill off the entire tree.
Here is an article that will help you to care for Yucca outdoors: