What it does
Psycho Cut is a Psychic-type physical move with 100% accuracy. Every time you use it, your critical hit rate goes up by one stage. Stack that with a base crit rate or abilities that further raise crits, and the probability becomes relevant within a few turns.
Physical Psychic moves are uncommon — most Psychic attacks are Special. For physical attackers like Gallade, Psycho Cut is the clean STAB option that actually uses their Attack stat rather than the weaker Special Attack.
It's a slicing move. That means Sharpness applies — the same boost that affects Dragon Claw. Gallade has Sharpness, which turns Psycho Cut from a solid move into its core STAB at boosted power.
Note that Psycho Cut targets Physical Defense, not Special Defense. Against physically bulky targets, it performs worse; against specially defensive targets with lower Physical Defense, it performs better.
Who runs it
Gallade at 97% always runs it. Fighting/Psychic physical attacker, high Attack, and Sharpness. Psycho Cut is its Psychic STAB, Close Combat or Drain Punch is its Fighting STAB, and the combination covers a wide range of opposing types cleanly.
Medicham at 78% pairs it with Pure Power, which doubles the effective Attack stat. At that point Psycho Cut is hitting extremely hard even before crits come into play. The crit accumulation is just extra on top of already massive base damage.
Absol at 15% is the coverage case — not STAB, but Super Luck stacks with Psycho Cut's crit-raising property, creating very high crit chances over time. Speed is middling, so priority management matters.
How to use it
In doubles, Psycho Cut is a precision single-target physical hit. The common pairing is a Fake Out lead locking down one opposing Pokémon while Gallade fires Psycho Cut at the other — full damage, uncontested action on turn one.
With Sharpness active, the power is high enough that you don't need to fish for crits. Use it as your main Psychic-type damage tool and treat the crit chance as a bonus.
Tips & strategy
Don't hold back Psycho Cut fishing for a crit if normal damage already KOs or brings the target low enough for a partner to clean up. Crits feel good but they shouldn't change when you fire the move — only whether you need the extra damage to seal a KO.
Fighting-type coverage rounds out what Gallade threatens. The Psychic/Fighting combination hits a lot of types for neutral or better, leaving very few hard counters.