The phrase is used as advice for impatient drivers (usually impatient, incompetant yuppy sorts in overly expensive cars) who hesitate when a much slower car approaches the intersection (usually driven by an old fart with a handicapped sign on the mirror). If the yuppy waits, he will inevitably be trapped behind the slow old fart for a long time. Thus the advice, "first cut them off, then flip them off" intended to not only offend the other driver by cutting them off, but also to infuriate them by giving them "the bird" immediately thereafter. A totally un-called-for move which is very hilarious, it is also summed up by the phrase, "those who hesitate, wait". Either phrase perhaps best summarizes the attitude of extreme, offensive driving- skills not taught in your average Driver's Ed Class.
"Frank slowed down at the intersection, but when he saw that handicapped sign on the approaching car in the cross traffic, he gunned it without stopping. As the tires squealed around the corner, he rolled the window down and flipped off the cross traffic. I asked him what the hell he was doing and he replied, "first cut them off, then flip them off". Man, Frank is an asshole!"