Looks like celastrus orbiculatus, Oriental bittersweet. A terrible invasive and very vigorous. Unless you're very persistent, cutting back a specimen of that size isn't enough. I would cut it close to the ground, use a sharp knife or pruners to strip as much bark as you can off of the stump and then paint the stump with undiluted roundup or brush-b-gon. With either herbicide, buy the most concentrated possible (the ideal is something with a high percentage--60%+--of triclopyr). Keep an eye out for regrowth and repeat as necessary.