Dividing your existing plants is a great way to control their size and keep them healthy and beautiful. It can also help you enlarge your garden and create a cohesive design through repeated plants. With that being said, you should not divide your shrubs the way you would divide your perennials.
(Shown: Fothergilla major shrub)
Unlike most perennials, shrubs are woody plants—they do not die back to the ground after the growing season comes to an end. Their woody root systems tend to not do well when divided—unlike many perennials that have fibrous root systems that typically will bounce back rather quickly. Even if you successfully “divide” a shrub, the divisions most likely will not develop a nice, natural shape—as a result of undeveloped sections where the division could not regenerate properly.
However, an exception is for shrubs that produce “suckers”, or small new plants that come up from a horizontal root, like lilacs. Of course, with suckers you aren’t really dividing them; you just dig out the suckers and replant them elsewhere, without disturbing the mother shrub.
If you really want to increase the amount of your shrubs without purchasing more, try propagating them through softwood cuttings, root cuttings or hardwood cuttings. Keep in mind proper propagation will vary depending on the individual needs of your specific shrub variety.
Related: when to divide your perennials.
The Horticulture Smart Gardening Techniques: Shrubs is an insightful PDF with step-by-step instructions for various shrub-related projects.
Learn how to properly care for and grow healthy foliage plants with the Smart Gardening Techniques: Foliage Plants.
Discover everything you need to know about growing perennials with the Garden How-To University: Growing Perennials.
Want to learn the correct ways to perform necessary garden chores? Check out the Garden How-To University: Honing Your Essential Skills.
Keep your garden thriving beautifully with helpful tips from the Garden How-To University: Gardening From A to Z.