There are numerous synonyms for the phrase "headed off," which essentially means to leave or depart from a particular place. One effective synonym is "set out," which implies a sense of purpose or intention behind the departure. Another option is "left," which is more straightforward and direct. "Embarked" can also be used to describe someone starting a journey or trip. "Begun" is a synonym that emphasizes the start of a new adventure or chapter in life, while "departed" carries a slightly more formal tone. "Moved on" and "made an exit" are also informal synonyms that can be used to mean the same thing.