Agree with Specialmom completely. She is 11 and thus in 5th grade or is a young child going into middle school (which could explain part of this). Cutting is very serious and does need to be dealt with. Talk with your school counselor if she is in middle school or you school principal if in elementary about getting help.
Your daughter needs crisis intervention. This is also abnormal for her young age. Not having a boyfriend at 11? Most parents wouldn't allow kids to have a boyfriend at 11. Is she hyper sexualized or anything like that? Why so boy crazy at this young age? Is there a father in her life? What kind of discipline do you use for the yelling back at you when she doesn't get her way? Cutting is dangerous and warrants immediate intervention especially for a young girl. I'd consider a psych evaluation with therapy involved to help overcome this. Good luck--- that must be really hard as a mom!