Assuming you mean the one on windshield, if it's a GS with On-Star on it unplug wiring, then there is a set-screw, I can't remember if its allen or torx..but loosen that and slide mirror up and out of anchor--which is glued on the glass and will stay there.
Speaking of OnStar, anybody that has it should be aware that it can be remotely activated by anybody with moderate hacking skills..including the Federal Gov't can be used to track your car and even listen in to conversations inside your car. I am NOT a paranoid, conspiracy-everywhere kind of guy that wears a aluminum foil hat. I had a 2004 Regal GS (that got stolen) a car my Dad gave me, and in 2006 (while he still drove it) OnStar went digital from Analog and wanted $200 for the conversion. Just a couple reasons to ditch On-Star anyway
Looking for a Used Regal in your area?
CarGurus has 5,428 nationwide Regal listings starting at $2,495.
Search Buick Regal Questions
Buick Regal Experts