Question
After the yucca's blooms have fell off, how soon should I wait to cut the stalk off? Or should I let nature take it's course and let it fall off naturally?

Answer
It's always best to remove a spent bloom on ANY plant, mainly to keep it from setting seed -- a high energy exercise that wastes resources.

Yuccas are no different.  Remove the finished stalk or hard stem as soon as the flower is past its prime and no longer attractive.

Your choice of methods is based on the kind of Yudda you have.  A short, single-trunk variety is easiest.  Just take a scissors and cut close to the base leaf rosette.

For blooms and stalks on Yucca filimentosa and Y. flaccida, which are considered the more unattractive used Yuccas, remove the stalk AND the leaf rosette (where the flower emerges).  Lower the stalk down until you see rooty tissue and cut through it to remove the stalk and the rosette.  New shoots will sprout and reflower within the next two years.

Fairly easy to do this.  Hope this answers your question.