I feel for you OP. I had one of these too, fortunately now grown up and left school, holding down a steady and responsible job.
Speak to the head of year or the senior teacher in charge of disciplinary policy. Ask that he or she is your conduit and contact for all incidents so that they can be tracked and collated, and that you are contacted by one person instead of many upset teachers. Yes teachers - I'm sure its horrible to be confronted by a dickhead in class, but its not much better to be yelled at about the horror you have spawned, when you are at work and entirely unable to address the situation in the moment.
I would definitely offer to go to lessons with your child. I wish I'd done that to see for myself and / or for the opportunity to call out child's shit there and then, instead of having the haranguing, and being left with the teacher's angst dumped my lap without opportunity to deal with at the earliest opportunity.
I was never entirely sure how or if additional punishment at home was successful. Definitely do not indulge or spoil, make life uncomfortable e.g. take the router to work with you, lock the xbox in your car's boot. But don't use punishments that hurt you too, e.g. threatening not to go away on holiday as a family when already pre-booked and paid for is unrealistic.
I gave teachers permission to punish as they saw fit. I wish they had had more old school hard bastards. What they did have was a slowly boiling pot of disciplinary points that mean one day your son will show up without a pen and that is the final 0.5 that sees him off-rolled for his GCSEs. Try and avoid that if possibly by working with one member of the senior staff.
If you can afford tutors get some in, to at least try and get 5 GSCEs passed so there are still choices available. And you will get some sense of control even if illusory. Even screwing up qualifications is not the life sentence it seems at the time.
Time is on your side. Your son will leave school and/or turn 18. They will find their choices limited by their previous behaviour and employers fortunately are more direct and clear cut than schools. No one wants to see your child suffer, but there is a tremendous relief still when it is not your call or deal anymore. There are some lessons that cannot be taught or explained, only experienced.
Whereas I loved my own time at my bog standard 1970s school, I now HATE schools as a result of this experience. They are a very specific type of environment that suits some animals but not others. The stupid pettiness of the right shoes, is not replicated in most workplaces where you can also talk shit every now and then, and also get up and go to the loo / cup of tea etc without putting your hand up.
In my time of trouble I found MaryZ's posts really helpful. She is not on Mumsnet much or at all? now, but she was the wise centre of the Teenagers board about 10 years ago. She has great advice on dealing with difficult teenagers and the judgement people will fling at you.
Finally please love more but care less about your son. School is a time limited relationship, but you and him are in for a longer haul, so as much as I didn't, be patient and calm in dealing with him, calling him out on his BEHAVIOUR and the impact it has on his classmates, teachers, you and himself. But refrain from name calling, labelling, "you always", "you'll never" The future is not ours to see.
I wish you well 
and it does end !