Looks like grape vine. It's got the woodiness and the curly Q. If others agree on the ID, I can tell you how to get rid of it....
The best way is to cut it at the base, and paint or spray roundup on the base. The rest you have to pull down as much as you can, but eventually the dead vine may shrivel enough and get blown out of the tree. (Words cannot describe how much I detest grape vine). It is completely invasive, so you have to cut every base stem, or it will spread. When you try to pull it down, watch your eyes, because it will whip back and whack you in the head. I usually wear eye protection. The key is to get it while it's growing, otherwise the roundup does not work. Just be careful of other plants when painting/spraying the roundup. If you only have the one vine, you may be ok with just chopping it off at the base and not spraying the roundup...
