The axe is a weapon cut from Retail Blockland, but is reintroduced in some mods. It is based off of a real lego toy "axe" for lego minifigures to hold. Unlike most of the weapons in Blockland0002, it was scrapped.
The axe has so far only officially appeared in Blockland0002, where it had identical attack speed to the sword, and did not play any sounds. Like many of the weapons in the Blockland beta, it did not deal damage, and was coded similarly to today's default weapons.