I would suggest using a weed killer. Arlene. Cut the vines back and paint the cuts with herbicide like weed-be-gone or roundup or any of the woody plant herbicides..
Put the cuttings in a plastic garbage bag and set them in the sun for a couple weeks. Don't let any of it get near a compost bin or another bed.
I have found 10 to 12 foot runners going in a number of directions. If you cut through a runner, it will start a new plant.
It isn't grape, but it is evil.
