My dd was off-rolled at school a few years' ago because of anxiety caused by a bully at school, she also had mental health issues.
If I could go back in time I would have dealt with it differently. Yes, off-rolling is illegal, certainly immoral and goes against OFSTED guidelines. But schools, the local authority, OFSTED don't care and nobody can make them do the right and legal thing and provide an education.
I spent far too long fighting for her legal right to an education, pointless meetings, letters etc. Looking back I should have got a 2nd, 3rd, 4th job to finance home education and tutors (to provide structure and accountability).
Every moment out of education counts at that age, it's not right, you shouldn't have to be doing this but it's the way the world is today. Very few people care. You or your DC didn't cause the problem but you have to be the one to solve it.
My dd eventually got 4 GCSE's, she was expected 11 GCSE's A/B's had she stayed at school as she was in the top sets. 4 GCSE's didn't allow her to go into further education so the authorities then called her a NEET but provided nothing to help. People are quick to judge even when they caused the failure by illegally withdrawing education.
Good luck with whatever you decide to do.