When I was a lumberjack, we occasionally faced a “lodger”—a tree that, despite a cutter’s skill and best intentions, gets hung up in another tree as it comes down.
Never try to free a lodger by cutting the supporting tree—that’s a life-shortening mistake. The simplest technique is to cut 3’–4′ off the base of the fallen tree. Cut down into the top side a few inches—stop before the chainsaw bar gets pinched—then up from below. (Cautions: never cut above your waist; stand on the side where the tree is less likely to fall; make sure that your legs and feet aren’t in harm’s way.) Sometimes the change of position or the impact of the butt end hitting the ground will dislodge the tree. You can repeat this cut a couple of times, but be careful: the more vertical the trunk becomes, the less predictable its fall.
If the lodger isn’t attached to the stump, you can try hooking a winch or a come-along to the trunk at a 90° angle. Wrap the winch cable once around the trunk to encourage it to roll as you pull it to the side. If the lodger doesn’t fall, then at least it will be clear of the stump—and easier to winch away from the tree that it’s caught in.