I have a Stirling Engine friend in Belgium who, with his school class builds Stirling Engines each year (he's a school teacher), his method is to(gently) grip the tube in the lathe chuck, and use a Dremel with a diamond cut off wheel, run the lathe slowly, and drip water on the area being cut.
The last time I cut a test tube, I made a wooden V block to rotate the tube on, and scored the tube with a glasiers diamond glass cutter.
Ian S C