To dream that you have a mustache when you don't actually have one, signifies that you are hiding an aspect of yourself. You are putting on a disguise or showing a different aspect of your personality.

To dream that you shave off your mustache, denotes that you are revealing your true self. You no longer have to hide under some disguise or some shield.

Alternatively, you will try to reinstate yourself to a position of honor and status and abandon your associations with illicit pleasures and evil companions.