It looks like Bristly Greenbrier/Smilax tamnoides. Here is a link with photos:
http://www.illinoiswildflowers...
Others may have a more accurate answer.
Edited to add:
Whichever kind of Smilax/Greenbrier it is, cutting the vine will not eradicate the plant. You will need to dig, dig, and dig some more. Get a crow bar, pry bar, pick ax or whatever tool it takes to remove the huge root mass. Use a Google Image search with the keyword 'greenbrier tubers' to see what is underground.
Edited to add link.
