Oh honestly, the medical profession make me so angry sometimes!
This is completely untrue - yes, it is slightly easier to remove it if AF is taking place, but it is by no means a requirement.
I had my Mirena for 5 years, no AF at all for 4.5 of those years. Went to private GP to have it removed who had this bizarre circular argument with me along the lines of:
Doc: You'll have to come back when AF is here
Me: But I haven't had AF for 4.5 years
Doc: Yes, but you'll have to wait for it to be here to remove it
Me: But I haven't had AF for 4.5 years
I also wanted a smear at the same time, I do understand that after taking the Mirena out, the cervical cells will be a bit battered so probably not going to get a clear result, but when I suggested that she take the smear before removing the Mirena I had a similarly ridiculous argument from her. It basically ended up with her saying that no woman with a Mirena could ever have a smear, she would have to have it removed and wait for 6 months. Seriously, I paid £195 for this - actually considering complaining.
But back to your question, no, please do not, under any circumstances remove it yourself - go back to the Doc and stand your ground.