A normal (tungsten carbide) wheel cutter should work OK down to about 0.5mm and give clean cuts. (Look after the cutting wheel – any chips out of its edge will be reflected in the glass cut quality).
You may struggle to break off the narrow edge of the slide – it might help to scribe all of the cut lines first (in a # pattern) then break the larger pieces, leaving the narrow edge until last. This avoids the tendency of the cut to run off at the start/end of the scribe line.
You may find that lubricant (white spirit, or similar) helps.
Keep everything clean…
Edit – if you can find a good edge on the diamond, that will work, too, but it does need to be a very sharp point to create a 'vent' in the glass. A worn diamond will scribe a line, but there won't be a vent under it and the glass won't break cleanly.
Edited By Andy Gray 3 on 13/11/2020 23:27:04