Catena Aurea on Matthew 3:7–10: Gregory the Great

Or, the axe signifies the Redeemer, who as an axe of halt and blade, so consisting of the Divine and human nature, is held by His human, but cuts by His Divine nature. And though this axe be laid at the root of the tree waiting in patience, it is yet seen what it will do; for each obstinate sinner who here neglects the fruit of good works, finds the fire of hell ready for him. Observe, the axe is laid to the root, not to the branches; for that when the children of wickedness are removed, the branches only of the unfruitful tree are cut away. But when the whole offspring with their parent is carried off, the unfruitful tree is cut down by the root, that there remain not whence the evil shoots should spring up again.