Cutting Edge and Plume Edge are a pair of single-target Mercury Psynergies available to both the Swordsman (Venus) and Swordsman (Mars) class series, as well as the Dragoon class series. This means the series is available to every character except Ivan and Sheba.
Cutting Edge: "Inflict damage with a shock wave": Cutting Edge is the weaker of the two Psynergies in the series. Cutting Edge appears visually as a blue shockwave being fired into the target as the user swings their weapon. The technique is available to the Swordsman, Defender and Cavalier classes in both versions of the Swordsman series, as well as the Dragoon class in its series. Statistically, Cutting Edge converts all damage to Mercury and has a base power equal to the caster's Attack stat plus 32. It costs 5 PP to use.
Plume Edge: "Attack with a foaming geyser": Plume Edge is the upgraded replacement to Cutting Edge. Visually, Plume Edge resembles a geyser erupting from beneath the foe, and the user striking them with their weapon while the enemy is suspended on top of the geyser. Upon reaching the Guardian (Venus Swordsman), Luminier (Mars Swordsman), or Templar (Dragoon) classes, the Psynergy takes over Cutting Edge. Statistically, Plume Edge converts all damage to Mercury and has a base power equal to the caster's Attack stat plus 80. It costs 15 PP to use.
While Cutting Edge underperforms relative to Planet Diver, it remains a valuable technique in the early stages of both games due to the higher PP rating and overall utility of the Swordsman class series compared to the Brute class series. If the player is leveled up enough for it to be available, it can help make short work of Saturos at Mercury Lighthouse. As Isaac will receive a Mercury-based artifact weapon, the Arctic Blade, at roughly the same time that Cutting Edge and Planet Diver become available, Cutting Edge becomes a useful attack from this point until the end of Lamakan Desert, particularly against the Mars-based enemies found in the desert. In The Lost Age, Jenna is a viable Swordsman candidate to give her early access to Ply and make use of her Pirate's Sword - when not healing, Cutting Edge thus becomes her most valuable offense. Against enemies resistant to Mercury, however, Cutting Edge loses much of its luster, and should be ignored in favor of a Venus or Mars Psynergy, if not a regular attack.