I don't know if this will be of any use to you but around 50 years ago i used to work for a company that produced Golay coils, something to do with early lasers. The lab technicians used to cut very thin glass ,around 1/64 thick, in two ways.
1. Bed the glass on something like the blue tac of the day so it was supported, and then score with a diamond, while still held on the blue tack press the two ends of the glass and snap.
2. As above but score the glass with a mini grinder, and snap or they may have cut right through. in either case she wore eye protection, water was used as a lubricant .
I only remember this because the girl lab technician was a right little goer, and before anyone complains, in those days it meant you could hold hands after going out with a girl for what seemed like a month of Sundays.
Paul.