This really does need professional support and I'm sorry it's so hard to access that. The PDA website course sounds useful.
The only book which helped me when my child was like this was Big Baffling Behaviours by Robyn Gobbel. It has a metaphor of a "Guard dog brain" for dysregulation and it has several stages of this with advice on how to respond within each stage. This helped enormously because, as a PP said, it's about breaking the cycle where you become reactive to them (which I have also done, and I completely understand as well as understanding your desperation not to let it happen again but not knowing how). I also like Conscious Discipline (both their own resources, and Mr. Chazz) because again they talk about 2 different "levels" of dysregulation and how you can recognise when children are moving back down from the most intense/violent state to a state where they are still emotional and still not likely to engage with anything but it is improving. Because otherwise when you're in the middle of a meltdown like this, it feels impossible and like there is no way out. Or you notice the shift to a lesser state of dysregulation and you jump the gun a bit and think it's time to start talking when it really isn't yet, they need a lot more time to come down to baseline. This can be especially frustrating because if you feel like you're getting out of it and then accidentally escalate them back up it feels relentless like it is never going to end.
I know it doesn't help in the moment but DS2 also said things about killing or violent acts which there was no way he could actually do but it was still upsetting to hear such things coming out of his mouth. What I think was going on with DS was that he was saying the most shocking/impactful thing he could imagine because words were what he could access at that moment, and his words were not literal but an expression of how big his feeling of anger/powerlessness was in that moment. Something I found which would sometimes help was to reply in a very matter of fact way such as saying things like "Nah, I don't think you could chop an arm off. Arm bones are really tough and you'd need a really big saw." This would often lead to a discussion about the mechanics of chopping off an arm which would bring him into a much calmer space because he would have moved from that defensive, watchdog brain into the curious, more logical (even though sometimes disturbingly detached!) kind of brain space. And eventually the discussion would come down to remind him anyway - we wouldn't ever chop someone's arm off in real life, because arms don't grow back, the only time someone's arm gets chopped off by a doctor is if the arm is very badly injured and can't be saved. Or sometimes it would go into a discussion of prison (ie what might happen to someone who chopped someone's arm off) and sometimes that would scare/worry him and then I would be able to reassure him that I am bigger and stronger than him and I would not let him chop anyone's arm off, and when he was older and bigger and stronger, he would be able to stop himself because grown ups can do that, even if they are very angry.
He does not get as dysregulated any more, because he has a diagnosis of ADHD (we live somewhere PDA is not diagnosed) and takes ADHD medication and this makes a world of difference. With the dysregulated behaviour, it often doesn't seem to follow a pattern because essentially I have noticed two things - firstly, it can build up over a series of days and basically if they have no outlet to relieve the dysregulation (and we never found one which worked reliably - I don't know if an OT specialising in sensory integration who could have come and observed us over several days at home might have been able to) then it will eventually reach a tipping point after which they can't do anything about it. And while DS used to be incredibly dysregulated by school, he also couldn't tell us what at school was bothering him and his accounts would frequently be jumbled and not make very much sense. School were no use because they didn't have the faintest idea what dysregulation was, so they couldn't look for clues themselves.
The second thing I noticed was that once he was past that tipping point, and sometimes the tipping point would be hit earlier than others, then it would frequently trigger a downward spiral, like a runaway train because he would completely disengage from the world and people didn't really understand (including me probably) and would keep trying to engage with him as though he was fully present and then get frustrated or wound up at his nonsensical response, which would increase his dysregulation. OR because his go-to when dysregulated is often to be incredibly loud and seek a reaction from anybody any way he could, his behaviour would irritate/escalate others around him and this would wind him up more. And when he was in that state he also couldn't access any interoceptive input, so he had no idea that he needed the toilet, or was too hot, or hungry or whatever. Sometimes he'd get little glimpses of it e.g. when a teacher was telling him off about something he'd realise he needed the toilet and ask to go, and they thought he was trying to avoid being told off and would say no/not right now, and he would understand this as meaning he wasn't allowed to go to the toilet at all, and would escalate again.
So if he was a bit dysregulated but "lucky" with it then it might dissipate on its own especially if it happened to be near a breaktime or similar, but if he was dysregulated and it happened to get latched onto by someone else then it would just flip into that escalating spiral. And sometimes if the dysregulation had built up over multiple days then it was less likely it would dissipate on its own.
So the key to managing dysregulation is basically 3-fold - you want to try and reduce sources of dysregulation in the environment generally, which might mean looking at tools to reduce sensory input, increasing predictability by using tools like a visual timetable/now and next board or having a very structured approach which is not deviated from, reducing demands, instructions being broken into steps, or him having tools for this (e.g. covering over part of a worksheet with a spare sheet of paper), more processing time, using communication strategies like declarative language or picture boards, trying to ensure basic needs like nutrition/sleep/etc are met whatever that means (e.g. a less balanced diet or melatonin). We have always had trying for a poo in the bedtime routine as well as it helps prevent constipation and that horrendous cycle. Increasing safety by prioritising relationships with key adults - can any adult at school spend 2 mins asking him about a special interest or just conversing with him without any demands in that conversation? Does he have a safe space/safe adult at school he is allowed to go to when he needs to? Is it a possibility for someone to be 1:1 with him for any portion of the day and help "translate" either his needs or the requests of the teacher/other adults/other children to him?
And try to protect some form of decompressing for him at home which he must have access to every single day. Whether this is something like a sensory swing or a lot of outdoor time or a sport or creative outlet or even something like Minecraft if that's what he's into. Don't get stuck in wondering whether it's a reward - it's a coping strategy.
And use de-escalation strategies in the moment - don't get caught up in the dysregulation yourself and contribute to the destructive spiral.
All MUCH easier said than done and may involve a lot of trial and error and unfortunately the "error" part of this isn't always immediately obvious so it is really really tough, the space you are in. Just know that you are not alone and there are others who have been there or are there.