The ability holder's attack stat cannot be reduced via moves like Growl or the ability Intimidate. It does not prevent stat decreases that are self-inflicted like with Superpower. It also does not protect against moves that swap stats like Power Split and Heart Swap.
Excluding Mawile, all Pokémon with this ability have notable pincers.
In Pokémon Emerald, if a Pokémon with Hyper Cutter used Cut on Tall Grass, it would reach 2 spaces away instead of just one. This ability was lost in future generations due to Cut no longer being able to cut Tall Grass.