Remove all branches with loose bark. Use your hands or clippers to break away these dead branches.
Determine which live branches to remove. Select any branches low on the tree that do not enhance the general shape of the tree or that run vertically like a vine up the trunk of the tree. Do not top the tree, and avoid cutting in excess of 15 percent of the live branches to prevent starving the tree.
Use hedge clippers to trim the branches 2 to 3 inches from the trunk. While mulberries are known as bleeders, the wounds do not need to be painted because the tree is dormant.
Place all trimmings into lawn bags, and discard according to local regulations.