Take a pair of garden clippers, and cut out a section about 6 inches in length of the vines a couple of feet off the ground. Same way to kill off ivy growing up and killing trees. And if you have the right agent, you can take a little and put it on the ground section you cut so they won't come back. :thumbsup:

Edit: You can get a spray bottle of Burnout II and spray it on the cut vine ends and the leaves will wilt die off in a matter of days. Its eco/bio friendly.