There are many different synonyms that one can use to replace the phrase "shut mouth." Some common options include "zip it," "keep quiet," "mum's the word," "hold your tongue," "button your lip," "hush up," and "cease speaking." Each of these phrases has its own unique connotation and tone, from the forceful "zip it" to the more gentle "mum's the word." Depending on the situation and the relationship between the speaker and the person being told to be quiet, different synonyms may be more appropriate and effective. It's always important to use language that is respectful and considerate in communication with others.