It must be so difficult to see your daughter suffering like this. My heart goes out to the two of you, and I hope that we can devise a plan together to get her the support she needs.
 
First, it is VERY important that you take your daughter's suicidal ideation very seriously. Whenever a child, teen, or adult speaks of suicide, we know that they are struggling to cope with the stressors they are facing, and we must listen. Therefore, I recommend that you do not delay in your efforts to understand and support your daughter.
 
Sit down with your daughter and explain that you understand it may be difficult for her to speak with you, but the time has come for her to get some help. Let her know that you understand things are difficult for her, but it does not have to be so hard. She can experience more happiness and joy in her life, and you plan to help. Provide her with the alternatives for help and ask her which she would prefer. Suggest that the two of you speak with the school counselor to discuss resources in the community (e.g., therapists, psychiatrists). If she would prefer to go directly to the community, talk with friends for referrals. Explain that you are looking for someone with expertise in teen issues, preferably self-injurious behavior. If you are limited financially, there are community mental health programs in most cities that offer sliding-fee scales (pay only what you can afford). Similarly, nearby universities often have training programs for therapists, and they may have a university counseling clinic for folks who are seeking therapeutic support at lower fees (typically pay only what you can). If you and your family prefer to speak with a spiritual leader in the community, you can also pursue that avenue.
 
It is important that you know that your daughter sounds sad and hopeless. She may, or may not, meet the criteria for depression, but she definitely needs help with her mood symptoms. Once she is feeling better, she can begin to work on more adaptive coping strategies. Individuals who cut themselves are typically overwhelmed by intense feelings, but they do not have a good way to manage them (e.g., talking with a friend, going for a walk or jog, hitting a pillow). Cutting helps to focus their feelings on a tangible injury, provides relief and can quickly become "addicting" as a way to cope with tough feelings. She needs to learn alternatives to dealing with the stresses of life. I included a couple of links to articles on the topic below.
 
Good luck in your efforts to find her support. Let us know if you have any additional questions.
 
L. Compian, Ph.D.
Counseling Psychologist
Education.com

your child has entered into teen age so be careful for handling her becoz if you ordered to her she wont obey any words of yours .... so keep on close touch with her self ... go friendly ....

she obviously needs attention from others, not just you...she seems like the kind of kid where things are just not good enough..make sure your supportive w/ her "expressing herself" in ways you may not approve...(Emo; ~ emotional dresser)...she needs to stand out in the crowd...it means alot to her apparently...cutting...a cry for attention...even though u may give her that, she needs something more. If everyone justs accepts her for who she is becoming, she'll start to accept herself. Good Luck & God Bless!

First of all make it clear to her that you don't judge her.  Let her know that you love her no matter what and that you are there for her to make things better, not to put more pressure on her.  Tell her that you won't pressure her, but that she should know that you are there for her to talk to, or that you will help her find someone who she feels more comfortable talking to.  Don't make this about you.  Don't blame yourself; it will only make her feel worse about herself and cause her to withdraw into herself more.  More than likely she feels badly about herself already.  I know that you feel guilty, but don't voice that to her; keep the solution about her.  Relieve her of responsibilities that seem to overwhelm her.  Likely, she is feeling a lot of pressure and that she isn't good enough.  
  
I started cutting when I was 12 years old.  It never fully goes away.  It wasn't until I turned 25 that I finally talked to my mother openly about it.  It wasn't until then that I really made headway in overcoming this disease.  It never fully goes away, but hopefully she'll at least know you're there to help her when she feels the urge.