In my experience most professors will do something to reflect the late submission of an assignment. Some might grade down a bit, offer more limited feedback (eg this is your grade, no qualitative feedback etc) and, of the lateness hasn't been agreed beforehand I know a good few who won't mark it at all. This is because they are busy, they mark assignments to a schedule and students, particularly post graduate students, are expected to be able to manage their time and work professionally.

In the circumstances I think he was more than fair, I know you don't think so and that's ok but your reaction to his perceived unfairness is way out of proportion and that's an issue if you plan a career working with people, especially vulnerable people. You can't be expected to have everything in place as a student therapist but the basics should be evident and managing yourself and your behaviour is a basic life skill. Others have given good advice about how to approach the disciplinary process, do read it and think about how you might best handle it given its got to where it has and you can't change that.