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Mirror Move allows the user to use the attack that your opponent has just used. The attack that's used from Mirror Move will retain all of its properties. If the opposing Pokémon has not used the attack command, this move will fail if Mirror Move is used first.
Mirror Move has little competitive use, since rarely is the move used by the opponent useful against said opponent. Furthermore, unlike Mimic, the move is only copied for that turn, giving the opponent too much control over the mirrored move.
Mimic is a similar move that copies a random move from target's moveset and replaces Mimic with the copied move.