Cut the bush back to ground level and apply 20% glysophosphate solution to each stump. Pulling is also effective, but if you don't get out all the roots it will come back.
Cutting without herbicide treatment does no good, it only comes back stronger with more stems. Most of the big bushes I've cut down (6-8" stems, 15-20' tall) require several treatments with herbicide during the first 6 months after cutting.
I'm fighting it in my woods we purchased 2 years ago. Slowly making progress on the most infested areas, but I'm loosing the war.
Good luck.