I build this after seeing similar saws made by Ron Soyland (http://tubecrafter.com/tubecrafter_015.htm) and Dalibor Farny (http://dalibor.farny.cz/another-photos/). I originally wanted it for accurately cutting glass tubing in the lathe, since my original "score and heat" method is a bit aggressive on thinner tubes. However, I've since found it useful for lots of things - the kerf width is very small, so it can cut quite easily, with some water as a lubricant.
The real secret is the blade - I never realised these were available. Search on EBay for "thin lapidary saw blade" and you'll get loads of results. I have a 4" diameter blade, but they also come in 6". Mine were only something like £12 for two blades. The diamond particles are swaged into notches around the edge of the blade, so it should last for quite a while.
For a spindle bearing, I used a NEMA17 stepper motor out an old disk drive. I removed the stator and made a plastic spacer. The spindle and bearings are very accurate and convenient to use. The hub must be very precise, so I turned and bored the hub all in one operation on the lathe to get it perfectly true. (Boring a 5mm hole is a bit tricky, but doable.)
A small DC motor plus a 555-based speed controller provides power. It's not very strong, but the saw doesn't need much.
The saw can either be mounted to a small table (actually the base from my "helping hand" for SMD soldering) or to a little rocking arrangement for use on the lathe. The blade can then be tipped gradually into the cut.
Quick video of operation: