I've got the same problem.
Theres a big one in my greenhouse that i keep cutting down and it just throws out new shoots and away it goes again.
I've rooted loads of the chopped off bits, one of them is 6ft tall and unfortunately its in the greenhouse border. I'm going to dig it up and make a yucca forest with that one and the rest that are in pots.
Mums link wont work for me so cant see what it says but they root easier if you leave the cuttings a day to scab over before you pot them on into sandy compost
I wrote about yuccas cuttings in my diary a couple of years ago, see below
If anyone has a yucca houseplant and would like to take a cutting from it they root really easily.
Cut off the bit for the cutting and pull the leaves from the stem. They overlap so start at the bottom and take them off in order. When you have a good length of stem leave it for 24hours or so to scab over, I have left them as long as 4days and they’ve still rooted. Then get a deep pot, I use the flower buckets from Morrison's which they sell off cheap and fill it with gritty compost.
Push the cutting in right up to the bottom leaves. You need enough stem in the pot to hold the whole thing steady. Give it good water and leave it to root.