It sounds like sensory/situational overload to me. Unfortunately in that situation, logic doesn't work because everything has become emotional/reactive. Punishments and rewards won't work here because she hasn't decided to misbehave, and is only reacting instinctively.

The easiest solution is for her to remove herself from the situation, but that can be difficult if she is doing something interesting/engaging. A helping hand in giving her space and time to process the situation could help. Talking through the situation after can help, but too soon after or too often can be detrimental, as you could exacerbate the overstimulation issue.

If you are able to recognise the symptoms before she reacts badly, you can step in and prevent the situation from getting worse. Many people with autism are not good at recognising their own feelings, so it's entirely possible that she doesn't even know that she's getting angry/frustrated until she snaps. At that point it's already too late for coping strategies. Teaching her to recognise her feelings early could help, but that takes a lot of time and practice.

One major difficulty is her age. As I've gotten older, I've found myself more able to use coping strategies. As a child, even though I knew the solutions, I was not always able to remember them at the right time, or go through with the steps when someone was telling me them.

Unfortunately I don't think there'll be a quick fix to this. It's possible that she will gradually learn to copy behaviours she sees, and learn to interact better with other, but it will always be an effort to do so.