The short answer is: No, you're not automatically fired from your psych residency, your match agreement may actually protect you, but you have some huge problems ahead.
The long answer:
You've mentioned "your visa transition", and that's going to be a huge problem. If you are on a J visa, then you have a big problem -- you can't stay in the US without a valid visa, being "out of status" may make it impossible to get a new visa, and you don't get the grace period. Same is true with an H visa, and for anyone on a family visa. If you're on an H, your employer may be required to pay for your return home
Unfortunately, it doesn't end there.
The match is binding on all parties. You matched to a psych program -- you must go there, and they must take you. Your application was honest when you submitted it and matched. Your application was not contingent upon completing the surgical PGY-1, since you'll be starting as a PGY-1 again. This assumes that the firing happened after the rank deadline -- if it happened beforehand, the program could make the argument that you were required to update them about this. That's a complicated argument, I could see it either way (the same way that if you get a S2 score after you've applied, it's your choice whether you want to release it or not. My sense is that a program would not be able to get a match waiver over this.
But, unfortunately I think you have bigger problems. Your program is certain to report this to the Board of Medicine. When you apply for a license in your new state (or if you're staying in your old state), they will see this. It's going to likely cause problems with getting a license -- and if you fail to get licensed, that will be a reason to waive your match
I agree that you had better reach out to your PD now. They are going to hear about this, and better coming from you. You've been vague about what happened but you had absolutely better address this head on, whatever it is. And if you are on a visa, you need to deal with that situation immediately.
Best case scenario is that you leave the US immediately (or get a visitor visa to stay), you still get licensed, and get to start your new program. But there are lots of problems ahead.
Last, you need to deal with whatever happened to cause this problem in the first place. Best of luck.