Question: what are all the enchantments you can put on a axe?
Answer: Curse of Vanishing. The Curse of Vanishing is the enchantment to use when you want your items to disappear after death. ... 
Bane of Arthropods. ... 
Fortune. ... 
Smite. ... 
Silk Touch. ... 
Efficiency. ... 
Sharpness. ... 
Unbreaking.