Now that's a difficult question. I think you could start by attempting to cancel negative thoughts with positive thoughts. I've heard of people writing down positive thoughts in response to their negative thoughts or saying them aloud. Some people say affirmations (positive things about oneself) every morning and/or night or throughout the day. They write down positive things and put them on sticky notes where they can see them. 

Cognitive behavioral therapy (CBT) is supposed to help with reworking how one thinks, as well. I'm not sure how feasible that is. Even regular therapy can help towards this.

You are a worthwhile human being so you just need to tweak your thinking so not everything about you is negative in your mind's eye. 

You can tell them you love them and that self-harm is an issue you're struggling to find words for but that it has very little to do with their behavior towards you. You don't self-harm because they've done something wrong, you self-harm because you're depressed or have anxiety or need to change the noise in your head to something more palatable or whatever your reason is and that even though you do give in and self-harm that it doesn't mean you're trying to reflect any of it on them. You're hurting and it's highly personal and it's not meant to punish them for what they might feel you feel is their wrongdoings.

You're definitely not alone. I've had friends and family feel that my self-harm is used to punish them or in response to things they've done and the only thing I can tell them is the truth, that it's meant to punish me. You'll eventually find the words to let your friends and family know how it is for you.

First off, you have to deep down want to stop. No sort of or maybe.

Then you have to realize nothing is going to replace it that isn't also unhealthy. That you're going to have to work through uncomfortable feelings and that it will ultimately get easier to do so without self-injury as a crutch.

Getting some form of therapy and, if your therapist deems it necessary, treatment of any mental illness you have (if you have one) would also be important. So that usually means telling people like your parents if you're a teen. If you're not, telling somebody like a significant other or good friend is important so you can get support through your treatment. If you're a teen a good circle of supportive people is helpful. Trying to do this all on your own makes it doubly difficult. 

For issues like this there's rarely a quick fix because you need to work out the issues behind the behavior. Basically, why you're self-injuring is important to figure out and try to resolve.

Quick things you can try is telling yourself you can self-injure in an hour if you feel the same way and try to see if you can put it off another hour (or longer) when that time passes by.

People hate people who have been chosen by whatever social system they belong to as being an outsider. There doesn't need to be anything wrong with them. They don't need to be anti-social, bad, mean, or really anything at all. There isn't always a reason for hate.

I'm sorry you're going through this. Have you looked into any anti-bullying groups for support? 

http://www.thetrevorproject.org/
http://www.pacer.org/bullying/
http://www.glsen.org/cgi-bin/iowa/all/home/index.html

I hope you can get through this. Take care!