I'd like to cut my steerer tube at home using a saw, without disconnecting and removing it, like this video. I'll just slowly, carefully cut it once, would that damage the bearings or anything? 2006 CAAD8 Optimo w/ Slice Ultra fork.

How would it hurt the bearings ?
Compare to riding down a bumpy road at 45 mph.

As long as you cut the steerer at the right spot and do so nice and straight across the real possibility of damage is to paint when the saw slips or goes through unrestrained. I suggest a beer can (pour the beer in a glass for after the cutting) wrapped around the top tube over some padding and taped in place to act as a guard. But seeing how easy it is to remove the fork one wonders why the risk to saw the steerer in the frame. Andy.

+1. Dropping the fork out is so easy to do on threadless setups and cutting a steerer is so much easier when the fork is not attached to a bike.

Just make sure you keep the headset bits in the right order and orientation.

if there is no better way of securing the fork while cutting, IMO, the bike is okay to use. just protect the frame and yourself.

Nothing wrong with cutting while the fork is installed. Use a sacrificial spacer thinner than the one you intend to finish with as a guide. That way if the cut drifts up against the spacer scoring it, you don't lose anything valuable. When finished, that same spacer makes a guide for dressing the cut square and clean with a file.

+1 And I wouldn't want all those metal shavings getting into my brakes, headset, etc.

I gotta admit the guy's a genius. He figured out how to use a bolt instead of a special tool to drive the star nut down. Points off for using a claw hammer.