Will your friends believe you cut away a vine as big as your arm or bigger' Pull the cut vine away from the base of the tree to where it's growing from the ground. Carefully recheck the 'girdled' area for any thin vines which may be snaked under bark. If you do not get all the vines, you haven't freed the tree. Leave the Ivy above the shoulder cut alone - it will whither and deteriorate. If an 'old growth' Ivy vine has a lot of leaves covering it, use your pruning saw to clear the leaves by making quick, vertical strokes parallel to the tree trunk -this will make it easier to see what you are doing.
Loppers work best on vines that are less than one inch in diameter.
The next step in freeing a tree is to make a lifesavor around it. After all that work, you don't want to give Ivy a head start by leaving it to grow next to the base of the tree.