I am guessing this plant is in the ground and not in a pot? Photos would help, if this is in an unusual spot or has a feature that makes it difficult to work with.
I suspect this is very much like dealing with the "pups" I get on my agave plants. No need to dig out the entire plant - I use a shovel to wiggle into the gap between the main plant to separate them some, then thrust the shovel through and cut it off. If you want to transplant this new plant let it grow large enough so it will be able to easily generate a new root system. If you simply want to prune this off to confine the size of the original plant, you don't need to be particularly delicate, it won't harm the larger main plant. (If you Google "propagate soft leaf yucca" you'll find lots of advice and videos).
_________________ Northwesterner
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