These ideas are not new. The original Frankenstein, for all of its monster-filled frames, had a scene of implied violence which was barely even seen but still left the audience of the day shocked. The scene was the shadow of Igor's dead body swinging from a rope. Psycho's most enduring images weren't of a monster at all, but Janet Leigh fighting against a silhouetted assailant in the shower. The power of that scene came not only from the acting, but the sound, music, and careful editing. But it had to start in the script.
Going outside the genre for a moment, Reservoir Dogs' infamous ear-cutting scene wasn't even shown in frame but rather panned away at that moment. It was much more intense for the audience because their own imaginations filled in the blanks.
But wait, you're saying. I don't have a James Cameron or Ridley Scott budget, nor am I one of those guys. That's the beauty of this. You don't need one to do or show less and take advantage of what I call the Audience Imagination Budget.
Sometimes I don't think we give the audience enough credit, either through a script or through the film itself. While striving for decades to come up with bigger and better ways to scare them with effects, the simplest of effects and lack thereof in some instances scares the audience more. Why?
Simply put: a viewer's mind has a bigger effects budget than a thousand Industrial Light & Magics. Tease them with a glimpse or only a part of the killer, keep things in the shadows as long as possible. It'll drive them crazy with anticipation. Use it to your advantage.
A very important lesson I learned was that it's as much as what you don't show as it is what you do show. That may seem like it works against the screenwriter's credo of “show, don't tell”, but it doesn't. It's knowing that there can be subtle but powerful nuances between what a character does and does not do in a scene that can tell volumes to the audience.
So when do we unleash a torrent of blood? Think of it like an exclamation point at the end of a sentence, not the sentence itself. I'm not espousing the idea that you drop blood altogether, although some movies were or are downright terrifying without a single drop spilled or even an on-screen death, such as Poltergeist.
What I am suggesting is that you, as a screenwriter, look over your horror story more carefully. How well do you truly know it? Is it gore for gore's sake, or is it there to add emphasis to your story?
If you think of these things ahead of time, then, when those moments of blood and gore do come up, they will be more like that exclamation point, capping off something that you've built up to, rather than letting the audience expect that it is going to happen every few minutes. Those moments then carry more weight to them and aren't as “cheap”.