I have more than a few miles of portage clearing under my belt and rely on a small top handle chain saw but that is not for everyone. I have never had a use for an axe on these endeavors. You start swinging that sharp edge in uncontrolled conditions and I feel there is too much danger of it glancing off a cut and inflicting injury. The small hand held saws available today are amazing. I also  carry an 18 inch fiskars pruner that easily cuts over an inch thick obstacles. It is really nice for reaching overhead and trimming stubs that could puncture soft sided canoes or cutting brush growing out of the rocks. When I am not toting a chainsaw and doing a clean sweep of the portage the goal is to drop  things low  enough to be stepped over. Often times cutting branches from under a fallen tree will allow it to drop lower. Other times looking at other things not allowing the tree to fall all the way to the ground can be productive. Lastly a small hand pruner able to cut three quarter inch sized live branches should be on your belt. On any portage there is always some maintenance that can be done with this simple tool as you return for another load.