The stump remover you are talking about is potassium nitrate, or saltpeter (same thing.) The reason you can't find it is probably because it can be used to make gunpowder.
If you want to kill the vines, I would use Garlon 4 (or generic equivalent Triclopyr) diluted 3:1 with diesel oil. Cut the vines and,paint the triclopyr on the fresh stumps. They shouldn't come back. That's how we kill buckthorn, which is an invasive tree that massively resprouts if you don't treat the stumps. If you just have a small amount to treat and don't want to buy a gallon of concentrated brush killer, look for a ready-to-apply product called Tordon RTU -- I think you can get it at Tractor Supply. Tordon may kill nearby plants, I don't know; it's a different chemical. I've never had that problem with the Garlon.
