If you are cut that bad, sutures are your friend. After they hit you with the local, it is just tug and tie from there.
It's the 'tug and tie' part, not the shot or the prospect of tying, that get's me. My sister fell through a glass door as a kid and had dozens of stitches. I had no problems looking at them, and it wasn't the blood as she fell through (I witnessed it, helped clean it up), it was imagining the tugging part, ewwwww, that gets me still. I have trouble with CSI scenes, too, but not the obviously gory ones. That's why I'm not a surgeon! ;-)