If these are actual trees and not shrubs - it appears many people call anything over their head (if even that tall) "trees" - most kinds are marred by being whacked back. Too bad you can't see where the bottoms of the vines are and cut there, that would be best.

I would cut the vine back until you find the source. You cannot cut back trees like you would a bush. Tree pruning must be done by someone who understands the proper method of pruning trees. Improper pruning of trees causes misshappen trees and leaves the trunk and branches at risk for disease and rot.