@UrbanWild,
Go to Lowes or HD and get a jug of Bayer Advanced Brush Killer. Cut the wisteria vines about 2 feet from the ground. Depending on how many you have, either put them into the jug, or pour the herbicide into a bucket or other suitable container. The plants will suck it up and die. The above ground stuff will die naturally and the underground, including any runners will be killed off by the herbicide. You can also spray it onto the leaves. BUT, if you choose to spray, make sure you do it on a wind-free day and that you can control the spray. Otherwise, you'll end up killing off something else as well. I've used it successfully on both wisteria and poison ivy.
