Yes, I forgot to mention the shop vac. That dust is indeed nasty, and probably not too good for your lungs !
The problem with the hack saw, even the fine tooth hobby (X-acto) type of saws, is the gap between the teeth. If that gap between the teeth, exceeds the wall thickness of the tube, then the saw will grab, pinch, and/or splinter the workpiece, just about every time, even with tape. Should you mess up, and splinter your cut, the cure is then just a few drops of CA's (cyanoacrylates), such as "Zap (Pink Label) Thin Viscosity" glue. This super thin glue (the thinner, the better), which is often referred to as "hot", will penetrate into even the smallest (even invisible) splits and/or tears in the carbon or fiberglass tubing. Just run a few drops of this stuff (it's like water) around the inside and outside, of the end of the tubing, and once it dries (it will dry very quickly), you can then lightly touch up the end of the tubing with some very fine sandpaper, should there be any objectionable irregularities. CAUTION: this stuff will permanently glue your fingers, hands, feet, or whatever, to anything they touch. Use with extreme caution, especially if you don't have a bottle of de-bonder on hand.
Another cure for fraying and splintering (if you don't have CA glue), is to dip the very tip end (1/8" - 1/4" or more) of the tube, into a mixture of two part epoxy glue. Then hold that end of the tube down (over a piece of newspaper), and gently heat it with a heat gun, or hair dryer. This will cause the thick epoxy glue, to become very thin, allowing it to run, and drip off of the end of the tube (preferably onto the piece of newspaper), but it will also seal up any splinters or cracks, that may be in the tubing. Again, once cured, the tube can be touched up with fine sandpaper, if need be. The only drawback to this method, is the curing time, which is usually longer than the CA's, but once done, it definitely won't splinter on you any more.