Place a piece of plastic underneath the vine to protect the grass or ground cover. Spray vines growing away from other vegetation using an herbicide that contains glyphosate. Glyphosate works by inhibiting the vine's ability to produce proteins. Remove the plastic to prevent smothering the vegetation.
Reapply the herbicide in 10 days. If you plant on planting vines in the location, wait two weeks to prevent soil residue from harming vine transplants. Use clippers to cut dead vines off of the fence.
Cut weedy vines growing near ornamental vines 6 inches from the soil. Dip a paint brush into the herbicide that contains glyphosate. Apply the herbicide to the cut portion of the stem growing from the ground.
Clip the weedy vine after it has died. Because the vine will have died, it will be easier to spot near the living ornamental vines. Signs of dead vines include wilting, browning and defoliation.
Spread a 3- to 4-inch layer of mulch in the area to prevent vines from sprouting or germinating their seeds.