If by self-injury you mean injuring yourself for pleasure (?) then, yes. For most guys I'm guessing that would be a major major turnoff. I'm turned off by it right now and I'm not even completely sure what you're talking about.
I think there's a pretty simple rule of thumb when it comes to men and deal breakers: if it involves non-sensual pain and the possibility of blood, then the majority of guys would pass. Of course, you have your S&M crowd out there who can always find a good reason to break out the chains, whips, and other associated-with-slavery apparel. And if that's your bag, baby, then hey, do you. I'd guess that you would need to find those individuals though because if you and I went out on a date and you decided to stab yourself with a rusty spoon because you couldn't resist the urge, I'd be out of there faster than you could say "ouch, that hurts so good!"
The main point is that you need to find out with any particular guy you're dating. Some guys are into butterflies and Disney films, others are into self-injury and like to slam their heads into mirrors. Hakuna matata!
It was written.