I've had mine on and off a few times. If you start by pressing the black "arm" toward the glass tilted at the same angle as one of the sides of the 3 sided nub, and push toward the glass as you turn clockwise, it should lock back on. Cushioned vice grips make it easier.
The rearview mirror in all of my vans over the years has been pretty useless as a mirror. I usually buy another mirror and then take one of the mirrors apart and use the mount for a radar detector or GPS. When I sell the van, I put the intact mirror back on.
Got it off, no problem! Ours is attached by three clips holding onto a hex-head attached to the windshield. A 60-degree twist in either direction releases the clips. 3-4 wraps of tape around the arm base protects it from channel-lock pliers.
Separating the mirror from its ball-arm isn't as easy. The ball is held in the mirror by a really beefy split ring that has to be pried off carefully if you want to save the mirror.
The ball on our Garmin GPS mount is a tad bigger than the ball on the mirror arm. So we applied some 1/2" heat-shrink tubing to enlarge the ball on the mirror arm. The diameter is just about perfect now and it seems to hold the Garmin bracket OK. Success!
Now once this rain stops, we can get back to insulating.
If you have youngsters that mirror is the eyes in the back of your head.
One time I pulled over in front of a police station and told the kids that if they couldn't behave that I was going to turn myself in for being a bad dad and no more vacation. mom would drive them home. My oldest one who was 6 raised her hand. What? I asked. Her question, "Can I have your Twinkie?"