I’ve heard they scorch the bottle neck with a glass cutter and with a little blunt force it snaps it off.
Maybe if you carefully loosened the cork first, to the point where it was about to pop on its own, then you could just knock it the rest of the way with a saber. But then, the French would tell you that you are not really "sabering" the bottle if you do it that way.
First, when "sabering" a bottle of champagne you DO NOT loosen the cork. Second, you DO NOT scorch or etch the bottle neck with a glass cutter. Third, yes, the "neck" of the bottle surround the cork breaks off so the cork and a small portion of the the bottle's neck flies off.
Opening the bottle of champagne with a saber is really a fairly simple "trick" to perform. You need a very cold bottle of champagne. The bottle must have been formed from two halves joined together (you have to look for the "seam") rather than a bottle without the seem. You expose the cork by removing the wrapping and "cage". You then hold the bottle at a 45 degree angle with one of the bottle seams facing up towards the sky. Then, using the blunt side of a saber or cutlass you slide the saber along the seam (in a quick and smooth motion) striking the raised portion of the neck causing the neck and cork to separate from the rest of the bottle. If done in one quick motion, the the raised neck portion of the bottle that surrounds the cork will break off cleanly. You are now free to drink the champagne.
Now this is a fun and fairly easy parlor trick to perform that usually gets applause and cheers from the onlookers but it should be performed with care and in an area with plenty of "open space" since the cork & bottle neck do fly off with relative velocity. Certainly you should always police up the cork and bottle neck after the trick and dispose of it properly.
