For those, I would just mow them down with my lawnmower set as high as it would go. Then when they sprout back out, spray the tender foliage with Roundup and be thru with them. YOU don't mention any kind of equipment that you may have but a weed eater with a steel gator blade will cut thru those easily. I use one on my fence line cutting small trees, vines etc and it works really well. The gator head is available at Walmart for about $20 and you could use it to weed the area around the vines also.
If you don't have a weedeater, they aren't that expensive either for less than $100 you could get all you need to do the job yourself in less than an hour.