As Scarlet is a better sword for the beginning of the game due to Finn's low pierce, Peppermint Battle Axe can be considered after Finn gets other pierce buffs outside of his sword. This allows Finn to increase the speed at which he farms cash from Thief King's Dagger and Mystery Cave Pick without damage, and also improves his general DPS against MOAB-Class Bloons.
It becomes outclassed by Thieves' Katana, which provides more speed and also has an ability which grants extra cash.
