Rosalba and Butterfly nailed it with their comments on what self harm can be for people, especially adolescents.
I was a cutter starting at the age of 13 until maybe 19-20 yo. For me it was a self-soothing act wherein the physical pain temporarily eased the overwhelming emotional pain/numbness dichotomy. It was something 'real' and 'controllable' for someone feeling so out of control of their life and/or emotions.
I think you handled it very well, Free. The hardest thing for me was thinking that my parents must have known (I was not careful about covering up) but were too wrapped up in their own issues to even care to confront me and steer me into getting help. By letting her know that you know, and that you love and support her, along with getting her to the regular therapy sessions, hopefully she will be able to find other coping strategies for what she is going through. I am so sorry that you are dealing with this - it must be so scary.