Round up, but make sure you have removed all suckers near the ground. You can actually spray the brown wood of the trunk with round up and not hurt the vine. I mean don't soak it. But if you hit anything green, shoots, suckers, etc., you can kill it. Also, never spray with lots of pressure or when windy. Trust me the mist will travel and you kill a vine or drastically hurt one. Once the vines are 3-5 yrs old, much harder to damage them, but anything green that you spray will die back.