Hi Shep,
I know it can be kept outside somewhere, but I'm in NE and it wouldn't make it here ;-) As far as cutting, wait till in active growth and you have a nice warm place to keep it and the cuttings. Cut the mainstem to the height you want and then treat the cutting ends with a rooting hormone. Allow to callus/dry for a while (at least a week, keep in a warm, dry, shady place), place the cut ends in a well drained, moist mix and keep warm. The mainstem should put out many new growing stems.
Dan
Lincoln, NE USDA 5

Some Yuccas are hardy outdoors here, some are not. The first step would need to be identifying the species. A common houseplant Yucca is Y. elephantipes which is not frost hardy.

You might want to post a picture on Name that Plant. Along with your present picture, you can post a picture of the attachment to the main trunk.
I have a similar plant called Yucca Cane. I root it by breaking off a branch & sticking it in water or soil. Even if it is rooted in water it transplants very easily. They grow over 20 ft tall & are very hardy.
This is what I break off & root:

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