Non-fruiting olive trees can withstand heavy pruning, usually to create an aesthetically pleasing shape for the tree, although most mature non-fruiting olive trees require very little in the way of pruning to maintain the health of the tree.
Remove all dead branches or any branches that appear diseased. To cut large, heavy branches, make a 1/2-inch deep cut with your saw on the underside of the branch within 2 inches of the trunk. Cut straight down through the branch from the top side approximately 3 inches beyond where you made your initial underside cut. In this way, when the branch begins to break it will snap off where the underside cut was made without stripping large quantities of bark from the tree. Once the branch has broken off, simply cut off the 3-inch stub.
Cut branches which are growing lower to the ground than you wish for the shape of tree that you desire. When cutting large branches always following the cutting directions in Step 1.
Cut branches that are growing sideways through the canopy of the tree.
Remove suckers, either using shears or by simply snapping them off with your hands. Suckers are smooth branches without true bark; they often grow from the roots or grow out of the trunk.
Top the tree if desired by cutting off no more than 1/3 of the main trunk.