In general, when you want to make a cut beam fall as directly as possible, you want to make a perfectly vertical cut across the beam. This means you should face a flat side of the beam as directly as possible, which also means you should try to cut from the same height as the beam. Any height difference will severely narrow your margin for error when making a vertical cut.
This looks pretty straight
Close, but no cigar
In this particular room, you can't cut from the same height as the beam, which makes saving all of the stones pretty impossible. One thing you can try to do is cut from directly beneath the beam, but due to the nature of the physics, you'll pretty much always lose at least one of the stones no matter how straight you cut.
Cutting from beneath
The good news is that this is the only situation in the entire game that I can think of where this happens. Most of the other stones are tucked away in hard-to-see corners, or perched on hard-to-reach ledges, and the ones you do have to cut down are usually on top of pillars (and that's a whole other question).
There is an easier way to get all of the stones on this particular beam. First, stand underneath it, and look to the far corner of the room. There's another beam hanging under a ledge. Cut it down, and use it to cross the gap. It might take you a few tries, since the gap is wider at that end of the room.
Now advance up the room normally until you're above the beam with the stones on it. Then you can jump to it and collect all of the stones.
Although, if you jump from here I think you'll die, so try jumping from a little ways down the ramp. And when I say 'jump' I really mean 'step off'. If you actually jump you'll probably die, depending on how high you are. Experiment a little.
Once you've collected the stones you can either jump, or cut the beam down with you on top of it (jumping may kill you, forgot to test that) and be on your way. Voila!
