Are they grapes or some kind of muscadine or scuppernong? In GA, muscadines and scuppernongs are much more common.
If muscadines or scuppernongs, I don't know if you can hurt the vines. I had some vines that were grown up onto a large 12x12 trellis that had to be 20 years old. The vines were grown on top of each other and were more than 1 1/2 feet thick on top, just a big mat of interwoven vines. I took a chainsaw and cut the trellis posts off, then cut the 2" vines off about 4 feet above the ground. I then hooked a chain to the trellis and pulled it off the posts and then pulled the remaining post stumps up. When I was done, I had a 2" diameter 4ft tall trunk, completely void of any green growth.
The next spring and summer, it put out a bunch of green vines. The second spring, I picked the longest and healthiest, and built a new trellis for them to grow on. I'm at the end of that second summer and they are starting to look like real vines again, even had a few scuppernongs this summer. I expect a good crop next summer.
I've done this with two different vines, removing 99.999% of the vine and have had great success. If I were you, I'd cut every vine off the main trunk back to two buds. If there are too many vines, say more than every 6 inches, I'd remove the smaller one completely.
Again, I'm not an expert, just know what's worked extremely well for me with two way overgrown vines. Also, you'll want to wait till late winter/very early spring to prune.
The Ison's Nursery web site has lots of info on muscadines and scuppernongs.