Russian ( Rushing!!?) Vine

There is a stump killer called 'Root Out' or something similar. It's Ammonium sulphamate. You put som on the stump once you've cut off the top growth, then put a plastic bag over the top of the stump to keep the rain off. I've found it effective for this kind of thing, and unlike glyphosate it doesn't need leaves on the plant for it to work.

 

I agree with Beechleaf. I've used it and it really is effective on everything