your question is not really making sense. if you want to reattach the mirror to the window, you don't remove the mount, or "button" as you call it,you simply rescrew it onto the mount. There is no removing of the mount itself. The rearview mirror is in that position for safety reasons.
I dont know of any solvent you can use to remove the mount, usually when you replace the windshield the mount is already attached to it. are you wanting to relocate the position of the rearview mirror or something? If you are wanting to only clean the area around the mirror, unscrew the mirror from the mount and take a toothbrush to the area around it then reattach the mirror to the mount. why you would want to remove the mount just to clean the windshield is beyond me.