What is causing this to turn black? Should I remove the entire piece, or can I just cut the black parts off?
I agree! Looks like it could be black beard algae. You could have brought it into your tank with some plants, it is usually a sign of the nutrient-light demand-supply needing some adjustment. Not very knowledgeable about it myself how that works, but you can keep it in check by removing as much as you can when you see it. Picking off affected leaves, cleaning ornaments with a brush if it is growing on them. BBA is very stubborn and hangs on for dear life, but I read it also responds well (getting killed off) to directly being dosed with liquid carbon.
As far as I know there aren't any critters that will eat it. At least not unless they are starvingly hungry. I always get a few spots on my Vallisneria, I just remove part of the leaves or trim the affected leaf down to the bottom.