This may not be the yucca you have, but nearly all species of that plant have similar instructions for transplanting of the pups. You can't hurt them, in fact you might have trouble killing them.

Transplant it late this fall at a time when conditions are moist. Dig as much of the root system as you can, then cut under the rest. You may even have to use a chain padded and wrapped around the ...

Dear Neil: I have a large yucca plant that I would like to move. Is it possible to dig and transplant them? A: Yes, but it’s certainly not easy. Their root systems are incredibly deep and tenacious.