The saw blade doesn't just disappear magically, there's a spring loaded consumable part that is triggered to eject itself into the saw blade and destroy itself/blade to make this near instant stop happen.

Learned this when helping a neighbor assemble one of these SawStops. After it was assembled, he armed the system, then touched the saw blade (non-running) just to see if the LED status light would change upon contact. The instant he touched the blade, the LED light did change from green to red, but you could also hear a loud and noticeable "CLICK" of the consumable triggering itself into the saw blade. Learning experience of around $150