When we use the term "open one's mouth," it usually means starting to speak or vocalize. There are many synonyms for this expression that can help clarify the context. One alternative is to say "speak up," which implies that the person needs to raise their voice to be heard. Another option is to use the phrase "begin to talk," which suggests starting a conversation. "Utter" also works, as it's a more formal way to indicate speaking. In some cases, "state" or "express" can also work as an alternative way to describe someone opening their mouth to say something specific.