Death would hardly be instantaneous from bleeding out. It would take a minute or more at the very least, all depending on which artery was cut and to what death. When bleeding out a person may begin thrashing about or convulsing or lay twitching all depending on so many different factors. And with a cut throat he may also start exhaling blood from the mouth ... none of these things are absolutely necessary to portray death in this method, but it is common.
But in a movie like this, low budget and all, a director probably won't go into such details. Too much work and cost and probably a bit too gruesome as well.