Punitory means something that involves punishment or retribution. If you are looking for synonyms for the word "punitorily," you can consider using words such as retributively, punitively, penalizing, correcting, disciplinary, corrective, chastening, castigatory, punitive, or vindictive. Each of these words has a different nuance that can convey the same meaning of punishment. For instance, "retributively" refers to punishment as a means of revenge, while "disciplinary" indicates punishment as a way of teaching and preventing future wrongdoing. Regardless of the synonym you choose, they all convey the same sense of punishment imposed as a result of breaking a rule or law.