Tiny and Big: Grandpa's Leftovers is a puzzle action game that stars Tiny, an inventor who had his Grandpa's underpants stolen by Big. The underwear provide tremendous powers and Tiny has to chase Big down through six levels to reclaim them. The game is built around destructible environments that can be reshaped by cutting them with a laser.
Most of the rocks and walls in the surroundings can be sliced in any direction, in any size and multiple times, and physics then cause the pieces to slide or fall apart. That way, puzzles need to be solved by creating constructions, removing objects, and devising custom platforms and bridges. Cutting is done by drawing a line with the mouse and determining the direction and the size. Once an item has been cut up, Tiny can push it in any direction or pull it using a grappling rope. Objects that are farther can also be shoved by shooting a rocket and then igniting it. In later levels Tiny is harassed by Big and needs to cut up rocks as they are hurled towards him. Big is the only opponent in the game and he is not present in all levels, the focus is mainly on progressing past obstacles in the environment and solving puzzles.
After the initial level where the mechanics are introduced, Tiny receives hints over the radio from his taxi robot. The game's art style has a comic book look with cel-shaded edges and visual sound words. Despite the sandbox possibilities most of the levels are set along a linear path, but with different options to approach the situation. The game's soundtrack is provided through fifteen tapes that are found throughout the game. Each tape provides an additional song and the player can cycle between them using a tape recorder. The general path is shown through collectible rocks and the game contains achievements.