Each year my back yard, house, exterior wires get completely over run by a vine.
Dear Gardener: Find the trunks of the vine where they come out of the ground. Saw or cut the trunk close to the ground and paint the cut surface of the trunk with undiluted herbicide such as Round Up. The cut surface of the trunk will carry the herbicide to the roots and kill the plant. Eventually the dead vine branches will fall or you may have to pull them down.