If you are talking about a stock mirror,it has to be taken apart to do it.
If you send it to me,I will do it for free if you pay the shipping.
There is a trick to getting inside,you have to use heat and finese,if not,you can break the glass......
I can tell you how to do it,but you have to do it right,or you will be buying a new one,and you cant just get the glass....
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When you say starts to swivel back, do you mean at the mid-arm bearing or just the mirror housing? If the whole arm is bending, that is a different problem than what Brendan is talking about... If it is the mirror, take him up on his offer!