There is a right way to saw off a limb from a tree.To begin with,make an undercut near the tree trunk.If you don't do those.when the limb falls,It will tear off the bark on the underside of the remaining branch as well as a strip form the trunk itself.The second cut can be made at a convenient place on the branch but close to the trunk,leaving a stub.Then cut the stub off flush with the tree.As the final step.cover the exposed raw wood with a good grade of paint.