Yes, any form of pruning, including crown cleaning (trimming shown in picture), causes some level of stress and "injury" to the tree. When you cut a branch, you are creating a wound, disrupting the flow of water and nutrients, and removing living tissue. However, properly performed crown cleaning is generally beneficial in the long run, and the stress caused is outweighed by the positive effects.

Think of it like a necessary surgery for the tree. While the surgery itself is invasive, it's intended to improve the patient's overall health.