My son was the same way until just recently (he's 7 now). He still has some anxiety when it comes time to get his hair cut but is better able to tolerate it now. Here are the tricks that worked for us:
* Don't say anything about him getting a hair cut in front of him. Children with ASD are literal thinkers and "cuts" hurt, therefore hair cuts must hurt also. It's okay to tell him that he is getting his hair trimmed or you are taking him to get his hair shortened but never a hair cut.
* Bring one of your husband's shirts or t-shirts to use as your son's cape. Those black smocks cause my son to have a gag reflex each and everytime. Shirts and t-shirts are less claustrophobic and more familiar. You can even have him chose which shirt he wants to use so that he can feel like he has more control over the situation.
* Bring a kid-sized chair for your son to sit in during the appointment. Those big chairs that go up and down are frightening for most kids who have SPD and body awareness issues.
* Have the hairstylist talk to your son in very simple terms before she does anything to your son. If she is using clippers, have her explain that the clippers sound like buzzing bees (if you don't think that will scare him) and let him touch and hold the clippers while they are on before they go anywhere near his head. He may not be able to talk just yet but, hopefully, his receptive vocabulary is good enough to grasp what she (and you) is trying to explain to him. But it is very important not to surprise him with sudden moves or not explain what is going on.
* Whatever his interest is, you will have to use it to redirect his attention during the appointment. For my son, it was animals and spelling. During the "hair trim," I kept my hands firmly but gently in my son's lap to keep him from getting up and talk to him about animals and how to spell their names (e.g., "c-o-w," "r-a-b-b-i-t"). He wasn't completely distracted but he was just enough so that the hairstylist was able to hustle through the trim.
* Reward him for his good behavior during the appointment. Talk to him about it before you even step foot in the salon and make sure that it is something that is a really, really special treat/toy that he doesn't have access to usually. Really sell it to him. If you need to, bring the toy or a picture of whatever the reward is going to be with you to the appointment so that you can have it there to remind him of what's waiting for him after the appointment.
* Of course, your son's objections are a sensory issue and frustration/confusion issue. If you are working with an OT about his SPD (hopefully you are), then talk to the OT about this because they are a great resource for information and kid-friendly solutions.
As I had mentioned, my son is 7 now and it wasn't until this last year when we stopped having major drama at each hair appointment. He still has a lot of anxiety when we go in for our hair appointment but I've found a wonderful hair stylist who knows how to relate to him and is patient and calm (two very important things). She's also young and pretty and I've found that my son really is more cooperative with girls that he thinks are cute. And there are a number of other reasons why he's doing better with hair trims now (OT, maturity, familiarity with the whole process).
Hopefully this will give you some ideas on how to troubleshoot the whole process and will take comfort in knowing that you are not alone. Wishing you and your son all the best. Take care.