Ask Mr. Smarty Plants

In all honesty, we think you are going to have to choose between the oak and the vine. If you drive through this part of the state in the Summer, you will often see a huge mound of grapevines. What you cannot see is the tree beneath that mound, and neither can the sun. With its big leaves, vigorous growth and vining capabilities, the grapevine will soon shade out the leaves of the tree it is using for support, and the tree will die. In the Winter, that vine is just straggling dead stalks hanging down, and if they're hanging down from a dead tree, that's even more unattractive. From your description, that's already a pretty vigorous example, and from personal experience, we can tell you it won't go quietly.

If you elect to keep the grapevine, you don't need to give it any care. It is a native plant to this area, and will grow with normal rainfall and sunlight, in the soil in your yard, without need for any maintenance at all, except a nice tree to climb on. The plant can be propagated by cuttings or seeds, and perhaps you would prefer to put it on a fence or trellis for the birds. Again from personal experience, we can tell you the mustang grape makes pretty good jelly, but it takes a LOT of sugar. 

If you decide to save the tree, get all the vines out of it as soon as you can. Cut off the vines fairly close to the ground and quickly paint the cut edge with a broad-spectrum herbicide. Don't spray it, and don't spill it-it can hurt the trees and other plants just as much. And you'll probably have to continue to grub out sprouts and even redo the herbicide painting for some time before the vine truly gives up and goes away.

From our Native Plant Image Gallery:

Vitis mustangensis

Vitis mustangensis

Vitis mustangensis