Use a woody bark herbicide, poison ivy killer, extra strong Roundup. Spray on mature leaves. Probably will more than one or two applications. Leave at least 2 weeks between aplications. Most likely many applications will be needed as new sprouts may pop up from roots that are twining under the ground. The roots are, probably, near as long & thick in diameter as the vine is. It will take diligence to eradicate all signs of the vine.
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