Don't change your image of her. She's still the same person. I cut once, when I was put on meds the first time.
Sometimes it's not the bullying, or the meds, it's that these things trigger dissociated shocks or trauma from the past. Anxiety is another issue that can cause youngsters to cut.
When someone cuts, it usually releases a bunch of chemicals and leads to a "release" or tiredness, similar to a "good cry." I think that sometimes it is hard to have a good cry, even though I feel like I need one. And I suspect that your granddaughter, at age 11, just reached that self-conscious age when even girls now believe they are "too old to cry" like a baby.
It is incredibly healing to access old, stuck memories that are holding one back and have a very babyish big, loud cry over them. There is a reason babies cry so much and don't need therapy. We forget how to breath properly and start to hold in our breath, creating anxiety. Same with crying, we forget that we need to cry or release emotions that over-whelm us.
Don't make her field like a freak. Lots of people cut, and in many cultures, it is a normal, everyday experience or is part of ceremonies. So many people cut and not many actually hurt themselves permanently. But it is a less helpful coping mechanism because it can push down the emotions rather than allow cognitive processing and reframing of experiences.
I think art therapy is a gentle thing for kids to do. Taking a fun art class or a new or old hobby you can share with her is healing.
For example, my grandpa used to make little wooden boats out of wood scraps and take me to a park with a small lake to try them out and see which ones will float. He attached a long string to a nail placed at the front and let me take them for a spin and have a simple picnic. When I got too old for that, he took me out on his sailboat and showed me his crab traps. I think sharing something that gives you a release, like a hobby or pastime, is a blessing and major form of love. She needs to see how real people find release, so that she can start finding her own. Meantime, she will feel the love in your choice to spend time with her.