This phrase has been around for a fairly short period of time; perhaps only since the early 1980s. It means, "Speed this up and let's get to the point."
It comes from the movies where the big ticket item is often the car, boat, airplane, whatever chase scene. Folks who are bored with the plot development features of the movie could be heard to say, "C'mon, cut to the chase."
One could even imagine some antsy, coked-up director saying the same thing in the editing room out in Hollywood.