Sorry to hear this. Did he have any extra support at school? Did the school do all they can to support him? If not, you've got grounds for an appeal against the permanent exclusion.
Local Authorities have a duty to ensure all children who want to attend school can, so it would be pretty unheard of for all schools to turn you down, he would have to be accepted into one.
Do you have any support from social services? You are able to refer yourself to the "early help team" and ask for support. They are able to help with a variety of things including behaviour, SEMH needs, school and home life. A big misconception is that social services are only for people who abuse their children, and that is absolutely not true. I work in a school and the majority of our students who have social service involvement have so because their families need extra support through no fault of their own.
Are there any SEN schools in your area that would look to accept him given his recent diagnosis?
Also, when he does get accepted into a school, ensure you make clear what his needs are and what help he will need from the school. All schools should have dedicated pastoral teams that do everything they can to make reasonable adjustments for students and support them to make better choices.
A permanent exclusion is obviously not a great thing, but the fact this has happened in year 7 is what tells me this could work out. I say this because students who are permanently excluded in year 9 or above generally only have the option of Pupil Referral Units (PRUs) unless they're lucky. Thankfully, in year 7 this is highly unlikely and another school should take him and put support in place.
Wishing you all the best OP, this is a hard situation and I'm sure you are doing a fantastic job 