time outs have always worked with mine. I explained why she was going there, how long she had to be there, after the designated time, went back and had her apologize, explained again why she was there and hugged it out.
As far as communication, maybe songs would work in helping her language skills. My ASD daughter learned better through songs, but flashcards also helped.

Ok first off. She is having a MELTDOWN. I thought the same it was a tantrum. But, its not. She is upset because she can not communicate. Communication is very and I mean very important to autistic people. Look up MELTDOWNS for autism, I will try to post something on here about the difference. You may want to start sign language or a communication board(pictures of things she likes or in her day to day living) That may help out a lot. Now, for the self injury that is apart of MELTDOWN. All I do is make sure everyone is safe. Here is what I make sure me son has, Consistency, Communication and Routine = CCR. Each and everyday. I pray this will help, feel free to asked me question. Have a good day.

Sometimes the word "no" can work better if you offer a replacement behavior or activity.

MyZett is absolutely right. It's about teaching what to do and managing her own anxiety/impact of Autism. ABA will help her and you. I know how hard it is. Hang in there.

*might not work for