Were you on probation first? Why exactly were you dismissed? Did you fail all of your courses, for instance?
Have you seen a therapist or anything, or do you have a diagnosis that would mean accommodations of some sort that you did not seek?
Your explanation isn’t really sufficient, sorry. I think you could take some community college classes and work and build up a record of success academically and in life, then apply to a 4 year school when you are ready.
I have a kid who did this and really experienced a turn around. You can do it, but I don’t think Purchase is going to let you back in as a result of any appeal unless you have a really good reason for failing, or a really good reason for them to believe you are going to change.
Believe me, I understand exactly what you mean about kind of freezing rather than trying out different paths. If this was a situation of depression or anxiety , or even ADHD, and a therapist could back that up, that might be different, but otherwise it could be expected to work at a course even if your interest had changed.