The gameplay of The Hyperstone Heist is heavily based on the second Ninja Turtles arcade game, Turtles in Time, which was also released for the Super NES during the same year. The controls are similar to Turtles in Time, but the ability to dash is now assigned to a specific button and the player can no longer throw enemies towards the screen.

There are a total of five stages ("New York City", "A Mysterious Ghost Ship", "Shredder's Hideout", "The Gauntlet", and "The Final Shell Shock"), which comprise a combination of new levels created specifically for this game and ones based on levels from the first arcade game and Turtles in Time.

The bosses include Leatherhead, Rocksteady (patterned after his appearance in the first Turtles arcade game), Tatsu (Shredder's right-hand man from the first two live-action films, who also appeared in TMNT: Manhattan Missions), Baxter Stockman (in his human form like in the first arcade game), Krang and Super Shredder.