IceQeen it is an absolute pleasure to offer some insight. I'm glad that I can be of some use! 
I can totally relate to your feelings of anxiety. I feel like I'm playing emotional Battleship most days. It's very easy when the ones I am working with are nice, lovely people. But the ones who are 'colder' and more prone to getting upset or distressed do press my anxiety buttons. Ironically, people on the spectrum suffer from extreme social anxiety, even though their approach can create anxiety in others. It's like an anxiety soup!
Cancelling your 121 was probably him not being able to cope with that meeting. Perhaps not, but I imagine this is the case. I'd put my money on it.
People on the spectrum are confusing because they can come across as abrupt and uncaring. Actually, they care a great deal. But it manifests itself differently.
Your boss will totally consume himself with worry about what people think about him. It will mostly tie him up in knots far more than anyone can imagine. But he will have learned to mask his anxiety and also, the veil of his ASD will make him seem more removed from his emotions and unable to simply just crack on with things and try to get along with everyone. It's not that he is unwilling to try and meet people half way. He can't. He is unable to, unless he himself has developed strategies over the years to do so.
Stress will make your boss shut down. In an autistic person, this can show itself in so many ways: tantrums, stimming (rocking back and forth/pacing up and down/drumming fingers/humming), but for an adult who has learned coping machansims to mask anxiety and stress, shutdowns can be i.e. abrupt cancellations of 121 meetings!
People on the spectrum don't like questions. It doesn't mean you can't ask questions, but again, less is more. Try to keep your questions closed-ended, so that he can answer them simply, concisely, and earnestly.
I have a funny little story. I gave one of my year 6 pupils a Christmas card, which he declined by saying, "No thanks, Miss. I already have too many. I don't need any more."
That's just so spectrummy. 
He wasn't ungrateful in the least. His cup was simply full.
A neurotypical person would smile politely, take the card, say thank you, and move on (it could even end up in the recycling bin on its way home).
I quite like the directness of people on the spectrum. They are rarely malicious or manipulative. This is something I appreciate greatly. They tend not to double cross.
Yet it can be very stressful for you, for example, because you will always be approaching your boss from a different angle. And you'll have to develop strategies in order to communicate successfully with him. You have to come up from behind, tiptoeing.
I think two of my most useful stock phrases are: It's good to see you.
And also, It will be ok. We can make this ok.
Basically, reminding them that they are good people (their moral compass tends to run really high) and constant calming reassurances keeps stress levels on low.
What you don't need to do is bend your brain and wreck your health trying to make a silk purse out of a sow's ear. So try your best and remember, your job description never said "compromise your happiness and sense of well-being to accommodate a terrible boss."
Look after number 1, OP! That's top priority here!