The tip of all stems has a rapidly growing group of cells. Divisions of these cells (the meristem) results in elongation of the stem. These meristems also produce a hormone, auxin, which inhibits the growth of other buds. Such a mechanism insures that the leaves produced at the growing tip of the stem will not be shaded out by competitive stems and branches.
When stems are pruned the apical tips are removed and so too is the source of this inhibitory auxin. Dormant buds sprout and branching occurs. When you prune a shrub you are removing these auxin factories and stimulating the buds that will produce lateral branches.
Kudzu doesn't need such encouragement and neither does English ivy and other viny species. Pruning the vines alone without also destroying the buds that produce new branches can make the problem worse. These buds are found at the swollen base of each leaf and on the root crowns.
Removing the root crown eliminates meristems that will produce new stems. Roots provide water, nutrients and stored food. But, without the meristems no new growth is possible. So the way to get rid of kudzu is to eliminate the buds, which means excising the root crowns.
Dr. Gillian Newberry