I love it! Plants are always doing things they're not supposed to be able to. Yuccas are pretty tough. In the south, anyway, the problem is usually getting rid of them, not worrying about their dying. Assuming that the parts you want to divide are already separate at the roots, dig down between them and cut apart the root - you'll probably need a saw. Cut the roots free around the piece you want to move - you can leave them several inches long - and stick it into the ground where you want it to be. You can let it harden off (dry) a couple of days before planting it, because it is a type of succulent, after all.
If the parts aren't separate at the roots, just cut off the piece you want to move and remove a bunch of the bottom leaves, to have a bare stem to replant. Let it dry a couple of days, then plant it in its new spot.
To cut off the yellow spikes, just reach down with your pruners to the spot where the stalk emerges from the plant stem, or as close to it as you can, and cut it. You can throw this part away.
By the way, are there other yuccas in your area? If not, you may have a sport. You might be able to find a grower interested in propagating it. You might ever get a variety named after you. Yuccas are really not supposed to be able to withstand sub-zero temps.
I live in Wisconsin. Have a Yucca plant in my front yard (west side). The plant has been in the ground more than 10 years. It produces 2 blooming stalks ever year. I want to dig it up and divide it, scare I will kill the plant. Need to learn how and when to cut off the old stalks and yellow spikes.
Here is an article dealing with yucca propagation: https://www.gardeningknowhow.com/ornamental/foliage/yucca/propagation-of-yucca-plant.htm
In addition, a small cutting with a piece of root can be planted and should grow. Yuccas bear both male and female parts in their flowers, and most varieties flower every year. I see that you live in Wisconsin. Do you have a potted yucca, or are you hoping to put one outdoors? They are native to the southwest, and are not hardy below 10 degrees F.