The term for cutting back a plant to encourage growth is pruning.
Pruning is the selective removal of branches, stems, buds, roots, or other plant parts. Gardeners use it to redirect growth, remove dead or diseased wood, improve a plant’s shape, and encourage flowers or fruit. Cutting a stem back to a healthy side branch or bud can stimulate new growth in a desired direction.
Two common approaches are reduction cuts, which shorten a branch to a suitable lateral branch, and removal cuts, which take a branch back to its point of origin. Pruning is not the same as indiscriminate topping: topping can leave large wounds and weaken a tree’s structure. Smaller, well-placed cuts are generally easier for woody plants to seal and compartmentalize.
Timing depends on the species and purpose. Fruit trees, roses, grapevines, shrubs, and herbaceous plants each have different pruning needs. A related natural process called self-pruning, or cladoptosis, occurs when a plant sheds twigs or branches that are no longer useful.