Chop through the trunk
Swing the axe with a real swing and keep cutting the same spot. When a cut leaves the top with nothing holding it, it falls. It shoves you but does not hurt you.
Cut up the log
The fallen trunk can be chopped further. Walk close to collect the wood. Clearing leaves now and then gives saplings to plant.
Better axes
Copper and iron axes take bigger bites and are made at the Forge. Axes wear out, see Tool wear.