Wildlife Spotting

Very invasive green/light green leafy plant. Please help identify and advise how to irradicate it without killing all vegetation? Vine like, has taken over my yard once again... At least 30-40 feet wide and 3-4 feet deep. I have cut this completely down several years in a row (including this spring) and it keeps coming back. It grows extremely fast and becomes like a canopy over everything from my privacy hedges to my laundry pole. It attaches itself with a curly spring looking stem that is brownish-red. The branches bend easily but are hard to break. It even creeps and grows along the ground. I have also noticed 'sprouts' coming up yards away from the plant/bush itself. It is killing everything in its path. Please, any help would be greatly appreciated!