Mature apricot trees should already be trained into a shape, so trimming focuses on maintaining a healthy, fruiting tree rather than on shaping the tree. Gardeners should prune apricot trees annually in the summertime or autumn once the fruit has been harvested, instead of during the dormant season. Apricots are highly susceptible to a fungus called Eutypa and, according to the University of California Davis, pruning in the summer or fall drastically reduces the chance of exposure to this fungus.
Check the branches of your apricot tree for dead, diseased or damaged limbs. Dead limbs feel brittle and don't sway in the wind. Diseased or damaged limbs bear discoloration, physical marking or cuts. This wood needs to be removed for the health of the tree.
Prune off the unhealthy wood by cutting it back to a "Y"-intersection, where the wood below is healthy, or prune it off at the intersection with the trunk. Cut it back at the base but don't cut into the trunk. In between cuts, spray your pruning tools with disinfectant spray to avoid spreading disease to other parts of the tree.
Remove any suckers growing from the tree's trunk or from old pruning cuts. Suckers are fast growing vegetative shoots that will never bear fruit.
Trim off branches that cross or rub against other branches. This wood places stress on the tree and shades the branches below. Also cut away branches that grow downward and shoots that grow vertically up.
Thin out the canopy to promote light and air circulation in the canopy. This helps ward off disease and promote healthy fruit development. Choose weak or old shoots and remove them at the base using your pruning tools. Oregon State University suggests removing wood that is three to four years old.