I have something similar, might even be the same thing, that I have been fighting for years. The best method I have found so far is to take a pair of needle nose pliars and use those to wrap the vine on. Get as low to the ground and as far into the shrub as you can that way, then pull the pliers out, taking the vine with you.
But I swear these things have a tuber or something because I never get more than a white chunk at the end and never a root, and they still come back.