In The Maw players control Frank, who in turn controls The Maw via an electrical leash that he uses keep him at his side. Gameplay involves guiding The Maw in specific directions to clear obstacles and complete levels. The Maw also has the ability to eat objects and creatures, taking on some of the properties of the thing it eats, such as breathing fire, flying, or simply growing in size. Players then use The Maw's increased abilities to navigate previously impossible sections of a level.

The Maw is set in a futuristic universe. The game begins with Frank, a pacifist bipedal alien, and The Maw, a purple one-eyed creature with large teeth, both having been captured by the Galactic Bounty Hunters. For unknown reasons the ship on which they are being held crash lands on a strange planet, killing all the crew. Alone, they set out for a communications tower in the distance while on the run from additional Galactic Bounty Hunters who have come to recapture them.