If possible, you should try to get the branch the hangers are coming from (typically perpendicular to the hanger) and better yet, the mother vine. It is somewhat amazing how an entire “bush” grows from a single vine.
Back in March I went in to a place I like in order to annihilate all these fuckers. My strategy is to just go to town on them with the hedge trimmer until I can reach the base and cut all the main trunks. It's amazing how big they get and how far they spread when nobody does anything about it for years.