But while it is advantageous to rid a healthy tree of its excess dead wood and unwanted dead branches, poorly executed pruning is equally bad if not worse for the well-being of your trees. Incorrectly pruning can result in a lengthy list of tree-health issues: including cankers, sun scald, frost cracks, insect borers, and more.
Amateur tree-pruners and home-gardeners tend to leave too much of the stub when cutting off branches. Once the extended stub dies off, it creates an easy gateway for disease pathogens and destructive insects to enter into the tree and wreak havoc.
Fortunately, making the correct pruning cut on a dead branch is typically much easier than de-limbing a live branch from a young tree. That is because you can distinguish between the dead wood and the live stalk much easier, as a ring of swollen tree flesh encircles the area in which living tree becomes dead branch. This circle is known as the "collar." The collar serves as a natural defense system.
When cutting off a dead branch, a perfect, flush cuts should occur just outside the collar, leaving as little of a stub as possible, but without damaging or removing any part of the collar (the natural defense barrier).

So there you have it. Now you can remove dead branches all on your own. But for rather large or particularly high dead branches, consider bringing in certified arborists a.k.a. "tree experts," like the ones at Hufnagel Tree, to do your pruning for you.