So of course D&D is a fantasy realm but it's tech is based on Medieval weapons and armor. If you do a quick google search on Medieval arrowheads you'll see that most of them, with the exception of those specifically designed to penetrate plate armor, have relatively broad, sharpened heads. A skilled archer is going to be able to hit a rope at a reasonable distance, at least well enough to slice it a bit and if it's holding up enough weight a good slice is all you're going to need for that rope to fray and unravel enough for it to snap. It may take a little time for enough strands to snap before it goes entirely but it's totally possible.
