I don't remember the dates on it (plus there's the issues of film slang varying by country and sometimes by city) but the reason is easy enough.

Until digital editing came about, films were literally assembled by cutting strips of processed film out and taping them together in order to create the finished product.

That's why the start/end of each shot is referred to as a "cut"- there was literally a cut in the film there. When a director announces "cut" on set, the meaning is twofold: in addition to being a signal to the actors to stop acting, that's where he wants the end of the shot to be.

Coincidentally, "action", at the start of the shot, was just to the actors. The phrase "Lights, Camera, Action!" is the order in which each had to be readied and cued. The camera thus began rolling before the actors began acting.

As for the hand-cutting-the-neck gesture, it would be used to communicate the need for a cut without making noise that would be picked up by the microphones on set. Since it implies decapitation, it probably goes back further outside of the film context. Since much of the very early days of film happened in France, maybe to the French revolution?