@Crystallizedring, welcome if you're new on here.
Just on the very brief description you have provided, it sounds like you need a specialist setting. No mainstream is going to be able to educate your DS effectively, in all honestly. Let's go one step at a time though.
Do you get DLA? This can help with paying for reports.
What reports do you have so far? and how recent?
Can you get what the head said in writing? Always get everything in writing. If they are reluctant, you can record conversations by emailing the day they happen or day after - e.g. 'Dear Mr Head, thank you for your very honest conversation today about how you felt that school x can't meet DS's needs, but felt you could keep him safe even though you can't provide him with a suitable education for his extensive set of needs'.
TBH I am surprised the school said they could meet needs when the LA consulted. Sometimes they are pressured to do so by the LA (more money saving).
Even without mediation you can still appeal. Do you know the timescale you need to appeal within? If that has run out you can raise a new ask to appeal but I have a feeling you may need to wait 6 months before re starting the process.
We will help you. You are not on your own. There is loads of knowledge here, and also we get it. The sleepless nights, the looking after a well loved child with high needs, plus trying to assert their rights.
It seems like a mountain but step by step you can get there (with us on your team). Your DS is entitled to a suitable education, not just being kept safe.