Oh dear. This brings back so many unhappy memories of ds's time in two schools that failed him the same way. He DID have a diagnosis and pupil profiles prepared by me and the Ed Psych/Outreach but they were ignored.
Walking away in stressful situations was my ds's way of coping too, and like others here it took a lot of hard work and training to get him to do that rather than lash out. None of this was supported by school staff which is why it took so long.
One of the schools he went to had an ASD unit and staff were supposedly 'very experienced' yet they operated a zero tolerance policy on this type of behaviour and it extended to the autistic children too, which was clearly ridiculous as they often couldn't grasp what they were doing wrong. His class teacher would rant on about minor misdemeanours, often still furious with him at the end of the day over something he'd done at morning break. He was a bag of nerves who didn't know what to do for the best.
I agree with the poster who said it's a reasonable punishment if school are providing proactive support as well and helping the child learn how to change the challenging behaviour, but punishment on its own doesn't work in these cases.
Yes, get everything in writing if you can. But recognise that your current school might just not grasp autism and understand how to work with ASD children. For some, inclusion means being the same as everyone else and they don't realise that some children simply can't do this. If this is the case at your school you may have to cut your losses and find somewhere that does understand and is prepared to give the support your dds needs.
We ended up HEing because we couldn't guarantee that what schools offer would actually be provided. I hope you find a solution.