How to cut ties with abusive supervisor?
I was going to just leave this as a comment, but I feel like it's worth an answer (even if it's effectively only one half of the answer), given the other current one:

Your current therapist (psychiatrist) has tried to guide you through this in a way that has caused you to mistrust them, by calling your account into doubt in a way that questions your grounding in reality and as a sole means of directing that line of inquiry, rather than something such as a strategy leading you to find (should they even exist) other symptoms that can serve as evidence of differences between what you recall and what may have actually occurred, should there even be any such discrepancies. All they have done is put you purely on the defensive and add an element of antagonism to a situation where you are already highly pressured from external sources, and where your issues stem from a situation where your trust was horribly abused. From how you are discussing the experience, it sounds like you are unlikely to receive meaningful therapy with them at this point, if trust with your therapist can't be re-established.

Find a good Clinical Psychologist. (PsyD or PhD)

If you do not have other, local avenues of seeking a referral you trust (and assuming that this is in the US), the APA maintains a Psychologist Locator service. You should probably first check if there aren't any state based referral networks available to you, if you can't get a personal referral from someone you trust. One avenue can be through your University's psychology department, not necessarily in terms of seeking care but at least a trusted referral.

A good psychologist will also be positioned to help you move on socially and professionally/academically from this as specific to your situation, with setting up both coping strategies and boundaries, and helping reflect on your own behavior, thoughts, and feelings in relation to both what happened and in moving forward from it. Not every psychologist is a perfect fit for everyone, and not every form of therapy as administered is a perfect fit personally or situationally: it's ok to tell a psychologist who you're trying to work with that things aren't working out with them and you feel you need to see someone else. Every clinical psychologist I personally know would be more than happy to refer you to a colleague who might be a better fit, in that situation.

If you feel you need medical (psychopharmaceutical) support to help manage things like immediately severe (acute) emotional issues while working on recovering, then seek a referral to a psychiatrist for that. There's nothing wrong with needing more or more immediate help than what therapy alone can offer, but I would suggest being upfront with your psychologist about that too (and usually they can be a good source of a referral to someone who can handle the medical side of things in a balanced manner) as it will affect how therapy proceeds in relation to corresponding changes.

A Psychologist will also be able to administer any well validated instruments that are appropriate, or refer you to someone who specializes in related testing, if there is a need for any. 


  I cannot relay what has happened since I am afraid it would be
  dismissed the same way as with my psychiatrist?


This is, ultimately, part of why this answer focuses on seeking out a psychologist to help you through this, because while your focus is on what happened (which is completely understandable), you may need to work on processing it as something unfair and unjust that happened to you and work on moving past it without relying on the particulars of the event as justification for how you choose to do so.

Sometimes when we are in the middle of a situation, all of our attention remains riveted on what happened, and we lose sight of simple answers to moving forward where what happened isn't a relevant matter to doing so. Some of @aparente001's answer focuses on suggestions that would fall under this.

I can think of at least a couple of Psychology Professors who also do clinical work, who I'm personally well acquainted with who have "seen it all" in academia and would give whatever story you have complete face value credence: if you can't find someone willing to give what happened to you a fair listening without immediately jumping to questioning your grounding in reality simply on a basis of what happened, then keep looking, because they are out there. At the same time, it's important to understand that questions of whether your perception of what happened might differ from the actual events is also not necessarily an attack on your state of mind. We are all prone to remembering things in ways that are not perfectly genuine to actual events. 

Someone who approaches that line of questioning should manage to do so in a way that doesn't leave you completely distrusting them, however.


  Things escalated to a point where I was on the receiving end of a racist declaration from him


It's unfortunate that you apparently have no documentation of your supervisor's behavior (although there may be more evidence of that behavior than you believe exists), because I realize the reality is that it can make filing a grievance difficult. I do think it's likely that you probably should file one either way (not about the letter, but about the behavior you experienced) from even the little you've relayed here, depending on the political situation within the department, but given how that may impact you professionally it's probably best to explore a discussion of that with someone you trust and with whom you can discuss it confidentially (which again, leads to the recommendation of seeking out a clinical psychologist you can form a strong working relationship with). I think if I had friends/allies in the department who were familiar with the Dean in particular and the political situation with your adviser in relation to the rest of the department, I would sound things out with them after receiving some counseling, and then make a decision of how to proceed with anything more formal based on their feedback.