Posted by Georgineer on 15/11/2020 16:10:54:
It occurs to me that it should be possible to mount a piece of glass to the lathe face plate with double-sided tape, or some other adhesive. Then an ordinary glass cutter could be mounted in the top slide and brought up until it touches the glass. A single turn of the chuck by hand should scribe the line, then the circle could be broken out in the ordinary way.
It can work – the same principle is used to cut out circles commercially. You need to start the break from the outer edge of the glass sheet and get this to run into the circle. It's likely to take quite a bit of practice.
For small diameters, the circles are broken out thermally – using cold metal cylinders roughly the same size as the circle which are placed in liquid nitrogen, then onto the glass (after scoring)
You might get somewhere using a metal cylinder from the deep freeze to get the circle to break out, but I still think you'd need to break the outer square of glass to release it.
Unless it's for entertainment value I would go to core drilling one out (very cheap diamond core drills are available on Amazon, etc. which will work fine, but *must* be used wet). Or trepanning one with a metal lap and loose carborundum powder – anything will do for a one-off: I used a boot polish tin to trepan out a secondary mirror for a telescope. Needs a fairly slow drive though (I wouldn't dream of doing it by hand).
Or just buy one! 
(Edit – you need just enough pressure on the cutter for it to create a vent in the glass – it will vary with the type of cutter. You will need to take into account some movement in the glass surface – i.e. the cutter cannot be rigidly mounted – it needs to float.)
Edited By Andy Gray 3 on 15/11/2020 21:43:45