I have an older adopted daughter who spent 7 yrs in a Russian orphanage. This is what we call "orphanage behavior". It comes from a child who is upset and doesn't have the proper coping skills to deal with their emotions. It is common among children who are raised in orphanages. This should be a big red flag to you about having your young child in daycare instead of home with her mama during these formative years. This is her way of sending you a strong signal that she is insecure and needs you for guidance and instruction. No - it is not normal - but it isn't unusual either.
Fortunately, you have the privilege of dealing with this at its onset and teaching your child the age appropriate coping skills. Ignoring the behavior is a bad idea. Left unaddressed, it can progress into self loathing, rages, and self mutilating - believe me, you don't want to go there. She has to learn that she cannot act out and misbehave. She also needs to learn appropriate coping skills for when she feels this way. You are blessed to be able to deal with this now and it should be relatively easy to handle.
When she starts one of these fits, recognize it is a way of showing her displeasure for being disciplined. Pick her up and hold her so that she cannot hit herself, sit with her on your lap and tell her kindly but firmly that "You may not treat my daughter this way. It is not OK to hit anyone - including yourself, or call them stupid." Repeat this instruction to her calmly as often as you must and hold her securely until the fit has passed.
This will give her the security she needs during the emotional storm. It also sets the standard for what is appropriate behavior in a gentle, but firm manner. After she has regained her composure (calm plus five minutes is best) then you need to calmly instruct her on what she could have done in the origional situation that would have been OK. You may even give her a chance to "Do Over" and role play the correct behavior with positive reassurance.
She's smart and no doubt has figured out that these emotional fits get a response from mama. Make sure your response is one that stops the behavior, establishes her safety and security, and instructs her on how to solve her problems. Otherwise, you will be stepping off into the realm of manipulation by fits. That's a real bad place to go. If she starts to rage again, repeat your response - calm + five minutes. She will test you, so be prepared to take the time to be consistant. Do NOT give in to an emotional response yourself or let her fits overpower your resolve to see it through. That will only strengthen her bad behavior and make it worse! So find a comfortable chair - a rocker is good - and prepare to be there awhile. Put out a box of Kleenex next to your chair to wipe the inevitable boogies and mentally prepare yourself ahead of time so you don't react out of your own emotion. YOU CAN DO THIS! :-)
Know that the end result will be a calm, sweet little girl who has learned to handle a tough emotion. She will feel so much more secure and you will be thankful for the peace it will bring to you both.
God bless you and hang in there mom! Be consistant and you can knock this one out in no time.