Not sure of your application, are we taking about exterior mirrors?
When I was restoring the interior rear view mirror for my 1962 TR4 I looked everywhere for a thin mirror and no one had them. I finally found exactly what I needed in the oddest place, TARGET.
The plastic handled mirrors they have in their cosmetic and hair product section have a thin mirror approximately 6 inches in diameter. If that meets your needs, be very careful when you are taking the mirror out of the plastic handle since it is glued in with a few dabs of silicone adhesive. I popped it out, cleaned the excess silicone off the back and took it to a local mirror shop where they cut it to size and ground the corners round using my original weathered mirror for the pattern.
When I was putting it in the mirror frame I cracked the first one and had to repeat the entire process again.
Let us know when you find what you need.