Like many vines, the oldest part of the trumpet vine plant gradually becomes woody, with a trunk that resembles a small tree. These large, mature plants are likely to send up "baby" plants through underground runners. If discovered when still small, these young plants can sometimes be pulled up and destroyed, but once a good root system is established, the task of eradicating a trumpet vine becomes more difficult. After cutting away the trunk, the roots should be dug out using a trowel or shovel. Small shoots that pop up in your lawn can usually be kept in check by keeping them mowed down with the grass. As a last resort, an herbicide can be applied. Choose the correct spray by checking the label to make sure trumpet vine is on the list of plants affected. Cut the vine back as close to the ground as possible and spray the stump. Then cover the stump with an old coffee can or something similar. If necessary, protect neighboring plants with a cardboard shield to avoid overspray when applying herbicide.