Any hardware store will sell diamond cutting discs for a Dremel. Just make sure you cut it in/under water.
With all due respect, that's making it more difficult than it need be. Cutting glass tubing is a simple matter: use a tubing cutter designed for glass. They're cheap. Probably cheaper than a diamond cutting disc for a Dremel. All you need to do is make a small score all the way around the tubing and snap it.
Here's an interesting example: glass tube cutting - YouTube