I'm guessing your program implemented some sort of remediation or similar process prior to dismissing you. I'd be curious as to what that consisted of (required therapy, etc). In my experience, programs usually dismiss students as a last resort, because they invest a lot in them and because high attrition raises eyebrows with APA accreditors. Programs might wonder what remediation steps you went through, why they were unsuccessful, and "what's changed" since then to prove your ability to be successful in this field. I think it will definitely be an uphill battle, but it's not impossible (though it may honestly be rather unlikely). Good luck!