Yes, there are 2 screws separating the base from the head. It is a little tough to get the mirror out of the head however. There are 2 screws holding the pivoting part to the head. If you tilt the mirror far to either side, you can see them. They are Phillips head screws, but I've had success with a somewhat smaller straight edge screw driver. You can try to hose them down with liquid wrench. You can't get a straight shot at either scew, but if you supply mucho pressure while you turn the screw driver, you should be able to get them out without stripping the head of the screws. It isn't much fun.
Mike