If you live in an area with wild grape vines, chances are good that you already know how destructive they can be. Eager for sun and seemingly impossible to stop, they will crawl over any and every other plant and tree in their endless quest to get to the sun. They choke out other plants and trees that you may have been trying to grow and are generally a nuisance. It is no surprise that you might want to kill them. Luckily, there are several ways to do it, only some of which involve chemicals.
Cut the vines. Do this in two places, once at your eyeline and once just above the ground, directly above where the vine goes into the earth and meets with its roots. Remove the vine parts that have been cut off and burn or discard. Do not compost, as they will have a chance to grow back and take root elsewhere. Wear thick, protective gardening gloves and safety goggles while you are cutting to avoid injury. Cutting the vines is most effective when done just prior to either step 2 or step 3.
Apply an herbicide according to the manufacturer's directions. The Washtenaw Conservation District in Michigan recommends Arsenal, Banvel CST, Crossbow, Garlon 3G, Pathway RTU, Roundup Ultra or Weedone CB as possible options. Crawford Conservation recommends Weedone 170, Tordon 101R, and Roundup as possible options.
Plant trees around the area where the grapevines were growing. Follow species instructions regarding the trees you are planting, as far as rules for spacing and depth go. Grapevines abhor shade, and will not react well to the erection of a shady canopy suddenly growing overhead. This method will take a few years, because the trees will take some time to grow. However, it is a good way to ensure that no grapevines grow in that area.