Another student, Jesse Sumpter, summarized an article by one Kathryn Walls on the axe in Sir Gawain.  She connects the axe with the words of John the Baptist in Matthew 3: The axe is already laid at the foot of the trees.  That fits the setting of the Green Knight’s first appearance - during the Christmas season, when not only the coming of Jesus but the coming of John would be celebrated.

Walls also points to Augustine’s interpretation of Matthew 3 in the light of Jesus’ words about fruit in Matthew 12.  Not every tree is cut down immediately; the axe is announced, the threat proclaimed, and then Israel is given time to produce fruit and escape burning.  So too Gawain, who has a year for penitence before the axe of the Green Knight “nirks” his neck.