Cut the kudzu vines as close to the ground as possible. Destroy any kudzu clippings, as new growth can form from clippings and mulch.
Use a controlled burn for any patches of ground that consist only of kudzu and nothing else (grass, seedings or other plants).
Aerate the ground and pull any kudzu vines carefully out by the root systems. Cut any kudzu-infested grassy areas closely when mowing for at least an entire season.
Apply for a permit from your local extension office to apply herbicides to the area infested with kudzu if all other methods have failed; you will not be able to use a herbicide if the kudzu is near any form of groundwater. Pay any fees for the permit -- which will vary by state. Apply the herbicide in an amount of 1 gallon per acre in spray form; avoid young trees, which could die as a result of certain herbicide applications. Search out herbicides that are acceptable for use with young trees, such as ones with glyphosate, clopyralid, metsulfuron or aminopyralid, if necessary.