Cut down the mesquite tree to a stump. Make the surface as level as possible for a uniform coverage of chemical.
Apply Roundup to the stump and thoroughly wet the surface of stumps that are less than 3 inches in diameter. The conducting tissues will carry the herbicide to the roots.
Wet only the 2 to 3 inches right next to the bark in trees that are more than 3 inches in diameter. Use the herbicide on freshly cut trees immediately following cutting. If you cannot use the herbicide right away, re-cut the top layer to expose fresh tree tissue before applying the herbicide.
Spray Roundup on mesquite shrub foliage to kill shrubs; this foliar treatment may be used on shrubs up to 15 feet tall. Spray to cover all leaves, but do not drench plants to the point of runoff.
Remove the stump after the plant is dead. Either grind the stump or pull it out by wrapping a chain around it and pulling out with a truck or tractor.