It would be interesting if it ever became possible to put our sons side by side - I see a lot of similarity. it may be superficial, or it may be that your son IS a lot like mine.
A few comments - you describe him as having some speech problems which the school initially treated, then they stopped because his speech was fine, but he still had troubles understanding.
This sounds like language delay to me, and to stop treatment because his speech is OK is wrong. There is a big difference between speech and language.
An example I often give - when difficult child 3 was a pre-schooler, we had neighbours with a son who was about a year older. A dear little boy, Steven - but one day he had a drowning accident which left him badly brain-damaged. Steven was in hospital for most of a year, the doctors expected him to be in a vegetative state - they thought he was, for a long time, because he was failing to respond to t heir instructions or questions. What they didn't know was that Steven had been brought up bilingual - Spanish & English. He WAS responding when spoken to in Spanish, but it is an uncommon language in Australia.
Two years later - Steven had a lot of physical problems and was totally aphasic - absolutely no speech whatsoever. But he would respond to instructions, his eyes would light up when he saw familiar people, and he would 'get' a joke and laugh. He was using a computer and could recognise some words as he saw them written - this was within normal range for written word recognition for his age. Basically, Steven had NO speech but normal language development.
Contrast to difficult child 3. He was highly musical, he would listen to songs on the radio and could mimic the entire song, compete with various background sounds which imposed themselves onto the words when he sang them. The words in his songs were recognisable but sounded 'blurred', like a child taught a song in a foreign language, who has no understanding of what the song means. In speech, difficult child 3 would not respond to instructions unless they were VERY simple and you had his full attention - he spoke lots of 'jargon' speech (his sister called it 'talking in scribble') but there was little or no meaningful communication.
Steven had a speech problem. difficult child 3 had a language problem.
Do you see the difference?
difficult child 3 developed language, through learning to read (unusual - it's called hyperlexia). He still can learn a new word through hearing it, but usually it's through reading it somewhere, either in a comic book or reading subtitles on a DVD. difficult child 3 has scored in t e normal range for language (expressive as well as receptive) for many years now. It is the HISTORY of language delay that is an important signpost in autism diagnosis.
difficult child 3 has had a lot of clashes at school, but because he had a diagnosis of autism before he began school, they had to recognise that a lot of behaviour problems are a facet of autism, they're not naughtiness. We took him out of school eventually, at least partly because there are always some teachers who don't understand and who don't want to, who treat this as naughtiness and punish the child when often it's their own failure to understand that has led to the child having a rage. difficult child 3 also gets very anxious, and a common response to his anxiety can be interpreted as misbehaviour, rudeness or rage. Mishandling of this will cause escalation to the point of physical violence.
I strongly urge you to get him assessed. You will need past records, including school records of language development and what they were working on with speech. Try to do more than just a school assessment - this is going to be tricky and I don't think the school has the facilities to dig deep enough. You need someone highly skilled for this, as he is 13 and has already adapted to his disability, whatever it is. This adaptation can mask the underlying disorder. The brighter the child, the more it is masked. This can look like they're no longer disabled, but this is a false image - it just means they can fake it well. They may not even be able to realise they are faking it until you sit and talk. difficult child 2 used to think everybody was like him.
So get early reports together. Get all school results, incident reports, previous assessments and doctors letters together. You probably need another speech pathology assessment (even if he now assesses as normal - I'm betting the expert will only find something very subtle, the last vestige of an early language delay) and a full, thorough psychometric assessment. if the school has done one in the past two years, take the detailed results to another psychologist who can do any remaining tests (this saves money, time and over-testing). A psychologist is also worth talking to about the social difficulties he is experiencing, but you may need a different psychologist - they often sub-specialise. But there's no harm in asking.
You may also then need a pediatrician or child psychiatrist.
I'm telling you what WE would need in Australia, because the picture is different in the US and I know your health care system is more like ours. Others here will give you the US picture - use whatever you can from either, whatever is relevant. But you need a confirmed diagnosis so you can get help. Right now he's being punished instead of helped. He is lashing out because he doesn't know what else to do. Anger and frustration are common. Depression becomes an even bigger issue in teen years.
And something to consider - check out the Pervasive Developmental Disorder (PDD) questionnaire on http://www.childbrain.com.
It's not officially diagnostic, but it can help gel ideas for you. You can also print out the results and take it to the experts for THEIR consideration. We can't diagnose on this site. The Pervasive Developmental Disorder (PDD) questionnaire cannot diagnose either, it has to be taken on board with a lot of other things, but it can give you a hint.
And for behaviour problems - get hold of "The Explosive Child" by Ross Greene. It was amazing how much it helped us. others here swear by it. Some people here didn't find it helped a lot, to keep it in perspective, but it's always worth a read. There is a discussion on it on Early Childhood forum on this site.
Good luck! Glad you found us!