The phrase "cutting a caper" is often used to describe someone's playful or mischievous behavior. However, there are several antonyms for this phrase that suggest a more serious, subdued demeanor. "Playing it straight" is one example of a phrase that suggests an absence of frivolity or humor. Similarly, "keeping a low profile" implies that one is intentionally avoiding attention or drawing too much notice to oneself. Other antonyms for "cutting a caper" might include phrases like "staying in line," "sticking to the rules," or "keeping a level head." All of these antonyms suggest a more sober or responsible attitude than "cutting a caper.