That new axe is better than chainsaw, but the range is extremely short.
The first hit is a quick single swipe with a long delay afterwards if you do nothing. The first hit might knock back.
For the second hit, you'll then swing the axe down doing normal (or reduced) damaged; then you'll roll the axe slowly along the ground doing multiple (I counted 6+ hits) weaker damage.
Unlike chainsaw, the axe does not combo well with other weapons. If you use another weapon before the axe, the saw effect won't hit as much. It still does decent damage, but it pushes the enemy slightly away on the downward strike. The most I've got it to hit after a combo is twice.
