I only have a few ideas/suggestions. First, I would definitely talk to her therapist to see what advice he/she has. This might need to be a conversation had with the therapist present so your daughter can talk about her fears.
Second, I would focus on how the process works and what the blood actually is (uterine lining). Hopefully by focusing on the fact that she's not actively bleeding, but is instead expelling unused cells (like shedding skin), maybe it will help some.
Third, maybe it would help her to know how you felt about learning about periods, your first period, how menstruation affects you now, etc. I think most women remember the first time they ever heard about periods and honestly, we dreaded it, were scared and talked about it with our friends (resulting in hearing horror stories from friend's older sisters). I think the more open you are about your feelings and how you feel each month, the more open she might be to ask questions and express her fears. You might even want to show her how to use a pad (unless that is too personal for you). We're open in our household and my 3 year old knows that I use pads sometimes, where they are kept, etc. Obviously, I haven't explained the ins-and-outs of menstruation to her, but I don't want her to be surprised and scared for the day that she's old enough to have the first conversation.
Being that she is 9, you probably don't want to wait much longer to first tell her about it. Girls are going through puberty sooner than ever and it would be horrible for her to learn about her first period by getting it before you've talked to her. I'm sure she would think she was bleeding to death if a scratch scares so badly.
Funny story... when my mom was 9 she had had a shot in her butt and she ended up with some blood on her panties. My grandma saw it and realized they needed to have "the talk" because she thought she had gotten her first period. It's probably best that it worked that way, because I think it was pretty common that the talk didn't happen until after the fact back then. Good luck! I feel for you, our little girl gets easily panicked about things too.