Cut and swab,
I've had to do it removing Groundsel bushes as they are not affected by foliar spray. Use a 50/50 mix of herbicide (very strong but most effective).
If you are going to attempt it, have the prepared poison mix ready to paint onto stump and top end of vine, as soon as sap appears the wound has 'healed' and will need to be re-cut. Speed is essential to ensure a good coating before the sap covers the cut. Sap works the same as our blood here and will rinse any infections or unwanted material out of the wound. Likewise air can get caught up in the top end of the vine and the poison will not be taken up properly (This is why you should cut bottom of stem on cut flowers to help prolong their cut-life)
An elephant never forgets....... I forgot what the elephant remembered...