How to explain blackballing by previous program in PhD application?
So here's what I see as the issue you need to overcome: If I'm told that a whole department or university conspired against a student to force them out, I usually tend to think that that is a silly allegation and that the person who makes this allegation is delusional. That's because it requires that a whole bunch of people (who also happen to be my colleagues!) would have had to act unethically, as opposed to just one person coming up with claims that have no factual basis but support their self-interest in believing that it's someone else's fault.

I have no idea which side is correct in your case, but as a member of an admission committee, a story like yours would certainly not make me excited about the candidate.

So you have two options in your explanations to the department you are applying to now:


You provide incontrovertible evidence that your claims really are what they are, and that the colleagues of the admissions committee members are all unethical blokes waging a vendetta. You may not have the space to sufficiently support your claims.
You make up some other explanation that sounds plausible for why you left that program. This may include "having had personal problems that you have since overcome through personal growth", or an admission that you really did something wrong but have come to understand by now why it was wrong and that you have learned from it. In either case, the explanation ought to be credible and probably ought to address the issue at hand in some way, though it can also be a bit nebulous.


The point I'm trying to make is that leaving a program, for whatever reason, carries with it a stigma that usually falls on the person who left the program, not the program itself. It is your job in the new application to address this.