I Love Lucy said:

If you cut them back, nothing is going to be growing above it unless,
sorry I don't get that part.

By that I meant, since you've severed the vine from it's roots (food
source), the vine above the cut will die, and then be easily removed.
Sorry, didn't mean to confuse. =)

I believe the common name for triclopyr is Brush-B-Gone.

HTH
--
Eggs

-A man who lives in a glass house should change in the basement.