I personally have not had any experience with grapes but here is a link to some information concerning grape transplants. It is possible and what's more it roots easily from scions.

www.ubcbotanicalgarden.org/forums/showthread.php?t=4513

Do you have a question? Do you want to know how to translant or do you want to know what kind of grape it is?

Hi Sens, we have successfully moved grape vines out of overgrown wooded areas by making sure to get enough root.
They have grown very well so you shouldn't have a problem with yours, they are "thugs" LOL Let us know how you make out with it , M

TY for the info,
I am looking to transplant the grape vine from the middle of our yard to the side, now it is not dormant. Would that matter if it is dormant or not?

If it's been there many years you can be sure it has an extensive root system. Ideally, it probably should be moved while dormant, either late fall or early spring (right after the ground thaws). It's probably a better idea to wait until spring, but in any case try to get a good chunk of root with it and be prepared for some dieback, it might die back down to the ground level and have to start over. Also, it might "sulk" for a year or two and not put on much growth.

Glen

You can easily root cuttings. In the fall, take off a branch, cut it into 2 ft pieces and sink them into a plant pot filled with washed sand, so that 2/3 of the stem is in the sand and the rest is above ground. Sink the pot into the garden. If it is very cold where you live, mulch with straw. In the spring, gently shake the cuttings out to the pot and you should have quite a few well-rooted stems, already to plant in your new bed. It always works for me.