How big is it and where is it growing? I had a very mature mass of the stuff to clear. The roots were huge, the growth immediately above the roots about 3" across. It was also growing against various dry stone walls, meaning it had rooted itself in the walls as it spread.
You have to attack the roots. I found each and every root in the ground, cut all the growth just above root level, scraped the roots in several spots to expose raw wood, and painted on Round-Up (at the specified dosage). It can take a couple of weeks, with another application if need be, but that takes care of the roots. It's a matter of finding all the roots.
Then, in my case, it was a matter of stripping it from the wall, sometimes levering it clear with a small crowbar, pulling it out where it had rooted itself, using Round-Up where I couldn't extract the roots.
If yours isn't growing against and into a wall, life will be easier.