I plan to file a petition to appeal academic dismissal at my school over my discontinuation from the psych program.?

so, when you decided to hide out, you gave them zero reason to make an exception.  stop hiding out.  frankly, most people in these positions see so many requests and petitions that they don't remember any in much detail -- and proper ethics means they don't talk about them.  -- grampa

You have asked variations of this question a number of times now, and you have received many good answers.  No one on YA can truthfully tell you what you want to hear, which is that your appeal will be successful.  The truth is you need to stop your endless planning, and instead actually file your appeal.  

What is a "discontinuation decision"? The term "discontinuation" is typically applied to programs, not individual students. The university might decide to discontinue, for example, the psychology program. 

Typically this is done with lots of warning, over several years, so the enrolled students have time to graduate with the degree; new students are not admitted to the program. Enrolled students are given the opportunity to switch majors. 

If this is what you mean, there is little chance an appeal would be successful. Universities only do this as a very last resort, because of a dire financial crisis. If they had any choice at all, they would not discontinue a program, so one student's appeal will have little effect. 

If you were suspended from the university entirely, for failure to make Satisfactory Academic Progress (e.g. GPA under 2.0 for more than one semester, not taking enough credits, etc. ), or for disciplinary reasons, then you can appeal the decision. The student handbook should provide the process. There may be a deadline before which you must file your appeal; for example, within 30 days after you received notice of the decision. 

You might want to contact an attorney that specializes in education issues to help with your appeal. Even if the basis for the suspension is completely objective (1.9 GPA for two semesters in a row, for example), it's not unlikely that the university failed to follow its process for the suspension somewhere along the line, and an attorney can help discover where. 

If you mean you were suspended from just the psychology major, but not from the university as a whole, I've never heard of that.