General:
* As open as a cavern (for a wide-open mouth)
* Like a trapdoor (for a mouth that's suddenly opened)
* Like a well (for a deep, open mouth)
* As soft as velvet (for a gentle, inviting mouth)
* Like a furnace (for a hot, burning mouth, perhaps from spicy food)
Specific:
* As red as a cherry (for a full, pouty mouth)
* Like a fish (for a mouth that's constantly opening and closing)
* As tight as a button (for a mouth that's closed firmly)
* Like a silent scream (for a mouth that's open wide but not speaking)
* As sharp as a knife (for a mouth that's speaking harshly or cruelly)
The best simile will depend on what you want to convey about the mouth.