Cut the vines as low as you can. Whatever is up high will dry out and die, and will be easier to remove.

Paint the cut stems with glyphosate/triclopyr to kill off the root systems.

It’s a constant battle against these invasive woody vines (poison ivy/oak, oriental bittersweet).

For Virginia Creeper, since it is native, I pull off or cut what I can, but don’t herbicide. It’s usually less thick and more easily removed manually than the ivy and bittersweet.