Thanks for writing. If it's an old, established grape, your best bet will be to dig it out of the ground.
You can also try spraying it with a brushkiller, but if it's old and established, it'll probably sprout back again and need to be sprayed again a few times.
If you simply want to keep it under control, you can find its base and cut it back to the ground once or twice a year.
---Justin, Senior Garden Editor, BHG.com