| Hi there yes Yucas can be cut at every height.They will resprout again in spring.There is no problem whatsoever.
Most sprout just under the cut area.So cut it as low as you want since the new shoots will appear just there on top of the decapitated stem.You have surely noticed that Yucas in the florists are such decapitated stems that have shoots at the top of them.They do just fine.It's the law of survival. The spots you describe may be some kind of rust(puccinia).It's a fungus that attack mostly monocotyledons.
Prune the plants drastically, spray them with copper and don't let many stems near to each other.Let the future plants be well ventilated between them.So space them not too close(through proper pruning) A little fertilization won't hurt either.Give them some such food in a month from now, so they will start in the new season strong. Observe if the spotting reappears in the new leaves later Good luck | 
