"Cuts a caper" is an idiomatic expression which means to behave in a frivolous or playful manner. The antonyms for "cuts a caper" would be behaving in a serious or restrained manner. Other opposite words for it could be acting solemnly or resolutely. One could also be on their best behavior, reserved or dignified. Examples of antonyms in this context would be being well-behaved, obeying the rules, or being calm and composed. Depending on the situation, alternatives might include behaving with decorum, acting professionally or maturely, and being reserved, polite, and courteous.