You can cut glass with scissors underwater because it creates a chemical reaction which lowers the energy needed to for cracks to propogate by a factor of 20. The reaction causes the cracks to propogate a million times faster. It makes it more difficult for large cracks to propogate.
Sauce and full explanation(3:29 - 4:30):
If I were going to apply that science to attempt it for a video:
I would thoroughly clean a bottle.
Fill the bottle with distilled water.
Place the bottle under container such as this:
(Filled with distilled water)
I would position it so that the distilled water would flow out of the valve/spigot into the mouth of the bottle and down the side. With the right flow rate and a little coaxing, the adhesion and cohesion properties of water would cause it completely cover the bottle and essentially encapsulate it in water.
Then try to chop it with thin blade(e.g. a grass machete) sharpened at a low angle.
With a mostly horizontal, or even slighly upward/downward, path in the swing, you might be able to cut it into two major pieces and preserve the path the blade took through the bottle. The edges wouldn't be perfect and some material would have shattered into tiny pieces, and therefore be missing, but it might not shatter the bottle.
Probably the purer the glass and the water the better. You would need a decent flow of water to avoid air gaps. You may want to try multiple thicknesses of bottles.
TLDR;

You could try a suspending a running water hose over a freshly consumed, water filled beer bottle so that it's covered in water and take a swing . A thick blade such as a real sword probably wouldn't work. Try a thin, high quality, heat treated machete.
If multiple tries of that doesn't work, try purer glass, purer water and/or different thicknesses of glass. I don't know if gluing the glass to a platform would help or hurt. Maybe add weight such as ball bearings in the bottom of the bottle to increase its inertia which would slow down the lateral movement of the bottle as the blade cuts through.