Not the buggy but the wifes MX5
The mirror has broken in the past and a poor quality replacement has been bodged onto the old base.
I am sure it isnt a sticky pad holding it on as I have tried sawing between it and the screen with very strong fishing line and it hasnt touched it.  Any bright ideas?
Cheers
Dave

depends how they stuck it, you could try warming it up to see if it softens.
my buggy one is now on with abraded glass area and metal filler as I got fed up of the pads failing along with other glues.
it may just be a break off and dress it up job.

Cheers Snoopy. I havent tried solvents or heat as it is on the black bit that is part of the screen so want to get it off without damaging that.
Might resort to one of those survivalist saw wires if everything else fails, its really difficult to get at as well with the steep slope on the screen

Pop in to a auto glass center and ask they might help worth a try 

Try dental floss.

Get some of the wife's nail varnish remover to melt the glue how I got mine off

Get some of the wife's nail varnish remover to melt the glue how I got mine off

Posh Nail varnish remover can contain lanolin, which can cause a few irritating smears, but some cheaper nail varnish removers are pretty much pure Acetone, which is certainly worth a try

Thanks guys, hadnt thought of nail varnish remover, I only use the good stuff so will have to get some from Poundland 
Dental floss, thats a thought, thinner than the fishing line I tried and pretty strong, maybe running that through with a drop of acetone on there will do the trick.
If all else fails will nip round to see Autoglass
I will let you know.

Pure acetone available from your local chemist for not a lot 

i did that once...nipped in to auto glass to get the mirror of... came home with a new windscreen after the bloke snapped it off the screen and broke the glass

[My Youtube channel]

And you know what....... That might ultimately be the answer.... Break the glass!

No get Autoglass to break the glass, am I right that they replaced the screen foc Shaggy as they broke it

As a matter of fact they did, as they didn't produce a waiver for incase of breakage upon removal of the mirror base on my rover