Sounds like a job for Roundup. (After you protect the good plants with tarps.)(Don't drag the tarps across the grass.)
I hope thorny vines does not include Canada thistle and poison ivy.
One important factor--do the vines spread by underground roots or rhizomes? If so, then the problem is a lot more difficult. It is important in beds to never let the weeds get over 6 inches tall. Beyond that and they will store food in the roots; the return growback is quicker.