Yikes! The base is bonded to the windshield . I can’t imagine that counting base can easily come off . I would bring your car to windshield replacement shop and let them have a look at the mounting base on the windshield . They can re-glue they back on for you with windshield adhesive.
Unfortunately I can’t because the car has been returned to the owner after the repair. Not sure why you want to see the side mirror? Do You mean the mirror on the driver or passenger door outside (side mirror) ?