Wild briars are one of the gardener's worst nightmares. The thorny vines grow rapidly and strangle surrounding plants. And due to their extensive root system, they're difficult to kill. Any of several techniques will kill wild briars, but they are most easily removed when you use all the methods together.
Repeatedly pruning wild briars can cause them to die out over time. You'll want to cut them back as close to the ground as possible. If the wild briars are tangled around other plants, cut back small sections of the vines and gently untangle them to minimise the damage inflicted on the other plants. Wear thick gloves to protect your hands from the thorns.
Spraying wild briars with herbicide -- preferably containing glyphosate -- is usually enough to kill them. The herbicide will kill any other plants growing near the wild briars, too. If plants are growing near the wild briars that you want to save, use a disposable foam brush to apply the herbicide to the stub of the stalk remaining after you cut back the briars.
Removing the roots of the wild briars stops them from growing back and spreading. Since wild briars have an extensive root system, you'll have to continuously remove the roots as you notice young briars growing. The roots are easier to remove if you cut back the briars and apply herbicide as close to the roots as possible. Wait a few days until the remaining stalk turns brown before removing the roots.
Place heavy pieces of cardboard where briars grow, or where you don't want them to grow, and cover the cardboard with thick layers of mulch. This works best if you cut back the briars first and apply herbicide. Removing the roots also decreases the chance of the wild briars growing back and penetrating the layers of cardboard and mulch.