Early on in the story, the narrator decides to deliberately cut out one of the eyes of his cat. This is a completely irrational and sadistic act of cruelty. Ironically, it is only really after one of its eyes is cut out by the narrator that the cat is able to see the narrator for the evil monster he really is. After losing its eye, the cat always flees "in extreme terror" whenever the narrator approaches.
The narrator's second act of sadistic cruelty is when he decides to kill his cat by hanging it from the neck. The narrator's explanation for this second act of cruelty is that he is overtaken by a "spirit of perverseness."
After this second act of cruelty, the narrator is haunted by the cat he has killed, and the cruelty he has inflicted upon the cat is returned to him in equal measure. First, he is haunted by the "apparition" of his dead cat. Secondly, he is tormented by a second cat, which doggedly haunts the narrator's every step, as if unwilling to allow the narrator to forget the crime he committed against the first cat. The narrator becomes terrified of the second cat, but he is unable to kill it, because he lives in "absolute dread of the beast."
Finally, the narrator becomes "wretched beyond the wretchedness of mere humanity." He is unable to rest, and he has nightmares "of unutterable fear." The spirit of the first cat further drives him to madness, and in an attempt to kill this second cat, the narrator instead kills his wife, who dares to intervene. He walls her corpse up in the cellar, unknowingly sealing the cat inside with her. And it is this second cat who alerts the police to the corpse's presence, howling in both "horror" and "triumph." For his crime, the narrator now waits in prison, consigned "to the hangman."
The irony of the story is thus that the narrator becomes the chief victim of his own cruelty, condemned to leave this world in the same horrid manner in which he inflicted upon his cat.