I've always told my ds's that I won't have them being bullied, but I won't have them being bullies either. I've been on both sides of bullying, having been bullied myself at school for having ginger hair, my ds's have been bullied at some points, and at other points they have been bullied themselves.
I think that it's sometimes difficult for some parents to talk about/care when their dc are being bullies. They either minimise it as only playing, or banter, or they think their dc is a little angel, or they think it's funny themselves and don't care. So it's good that you do care, and this is an important teaching moment.
In the past when my ds was bullying and being unkind, he was very young, about 7. His teacher took me aside and said that although he wasn't picking on any one particular child, he was generally going around pulling hair and standing on kid's hands when they were sitting on the carpet. I honestly came down on him like a ton of bricks on the way home from school, and took away his treats and his privileges that evening. I nipped it in the budd there and then, and we didn't have any more problems.
Likewise, when he was being bullied a short time later, I was taking it extremely seriously and straight up the school. Speaking to teachers, then head of year and then putting it in writing and taking it further each time when the school weren't taking it seriously.
My younger ds was trickier, because he has SEN, although the same rules apply to him. Luckily his head teacher was brilliant and called me and the other parent up to the school when he was pestering his dd, as they put it. Again, they were about 7. After we spoke about it, we brought in my ds and his dd, and I reminded ds about keeping his hands to himself and he apologised to the little girl. We didn't have any more problems. My younger ds has also been on the receiving end of bullying, which I take seriously and deal with as it comes up.
Sorry for the long post, but yes you absolutely need to take this behaviour extremely seriously. This is behaviour and a boundary you should have zero tolerance. You should work with the school, you ds should be made to apologise, in writing and verbally, and lose privileges, work to pay for a new blazer. This is absolutely a teaching moment, and an opportunity to set him on the right path. Hopefully these things will help the other child feel better and valued too. Being bullied can make you feel pretty worthless, and like no body cares, listens or takes you seriously.
Good luck op 