What beats psychic types in Pokemon Red?

Status moves help a lot too. Put Sabrina's Alakazam to sleep or paralyse it first, it outspeeds almost anything you'll have at that point, so taking its speed away is half the battle. Then the physical hitters can do their thing.

Gen 1 is cruel here. Ghost should be the answer but because of a bug ghost moves don't affect psychic types in Red at all, and the only bug moves you get are weak ones like Pin Missile. So type matchups won't save you. What works is hitting hard with physical normal moves, because Alakazam has huge Special but low Defense. A Snorlax or Tauros with Body Slam does it, so does anything big with Hyper Beam. Over-level a couple of mons a bit and bring full heals for the Venomoth and Mr. Mime.