However, Dig, Hyper Fang and ???-power moves are also allowed as an exception to this rule. Some examples of ???-power moves are Magnitude, Sonic Boom and Dragon Rage.
If any of these moves are learned by a single Pokemon, then that Pokemon should have no other offensive moves of the same type. e.g If Rattata has learned Hyper Fang, then he cannot have Tackle or Super Fang in his moveset. However, you may replace Hyper Fang with Super Fang for that matter. Moves like Mud Sport and Screech are still allowed since they don't deal damage.
Grass Knot, Fury Cutter, Rollout, Low Kick and the likes are also allowed. So long as their written Attack power is less than 70.