The narrative of Cat and Mouse is fairly abstract, moving the narrator's perspective flexibly and abruptly to different points in his memory. We know that we are dealing with a somewhat unreliable narrator, as reading his account becomes an exercise in navigating his disjointed thoughts. For example, he refers to the character Mahlke in both second and third person perspective, sometimes even switching mid-sentence.

The story involves the narrator ruminating on Mahlke from their time as children to his disappearance at the end of World War II. Much of the story takes place on a half-submerged wrecked ship where Pilenz (the narrator), Mahlke, and their friends meet every summer. Mahlke makes a sport of diving into the wreckage from the hatch to salvage parts of the ship.

At some point, Mahlke receives an Iron Cross for his service and returns to his school to give a speech. However, his school had previously expelled him for stealing an Iron Cross from a visiting officer and will not let him speak. Mahlke, who says that the only reason he entered the war was to give a speech at his school afterward, deserts his post. A mentally unwell Mahlke is pressured by an increasingly antagonistic Pilenz to dive into the wreckage once more, and he is not seen again.