I feel your pain. Some episodes with my son were a nightmare.
My son, who is now 20 (mentally about 15), went through the same issues with aggression. He would do something and then regret would set in not long after. Discussing the situation calmly after it happened, trying not to use the word "you" too much when discussing the situation ((keep it about the problem)), let him know most everyone has a temper, but.... ((I used to give examples of situations of when someone would get mad and had a bad outcome)), withholding privileges and explained what punishment means and that it wasn't to be mean to them but teach them that when someone does something bad then it causes something bad to happen as a result. I explained what the impulse emotion is and tried to work with him on that emotion as well as the anger.
It still happens occasionally, but it is MUCH better. He was/is on medication. But he still is learning "self " control. Most of the time now it is just verbal. He has come a long way.
Discussions, patience, praise when earned and positive thoughts through the learning process. :)

Good question. My son is 17 and has the same issues. We are trying different meds to regulate it but we keeping missing the mark