D..
Stop talking so much to her when she does this. Crying because she has been told no is her way of manipulating you. She also is working herself up, which at some point she cannot control.
So what to do? Show very little emotion. Send her to her room. Tell her that she can come out when she gets ahold of herself. No electronics, no TV (make sure there in no access to that in her room.) She can't be with anyone else during this.
When she has no audience, when you aren't trying to cajol her into stopping, when she absolutely knows that she will NEVER get what she wants by acting this way, when she loses the privilege of being somewhere other than her room, she will gradually stop.
When she cries because her feelings are hurt or she is physically in pain, when she cries for reasons that have nothing to do with being told no, that is the time to be empathetic with her, hug her, tell her that you are sorry that she is hurt. It's important to do this.
But if you don't deal with her manipulative and whipping herself up into a lather with tears NOW, she will pull this on people as a teen and it will be awful. Do it now.