Cut vines or briars 12 inches from the soil. Use gloves when handling briars to prevent getting pricked by thorns. Burn or throw away debris. Avoid composting to prevent spreading weed seeds.
Add 1 part water to 1 part herbicide concentrate. Use an herbicide that contains glyphosate. Dip a paintbrush into the diluted herbicide, and apply it to the cut portion of the vine or briar. Also apply the herbicide to any foliage on the briar or vine. Wait 10 days to reapply the herbicide if the vine or briar is still alive. Signs of plant death include browning foliage, defoliation and wilting.
Press a shovel 6 inches away from the base of the vine or briar and at a depth of 6 inches, to dig out the weed.
Spray vines and briars with the glyphosate herbicide on a windless day to prevent herbicide spray drift.
Plant bare areas in the yard with grass or other ornamental plants to prevent briars and vines from growing back.