First of all, NY does not have record expungement yet, and it means you will not be able to 'expunge' your criminal record. Second, what immigration status did you have at the time of the events described and when did it all happen? Third, it is important to know the exact basis for your deportation/removal. You must know that any person removed as an "aggravated felon" may NEVER return to the United States.
An alien deported as an aggravated felon is considered to be permanently inadmissible to the U.S., i.e. barred for life. However, the alien can still apply for a waiver on inadmissibility to allow for re-entry. Whether the waiver would be granted depends on why the alien was deported and why he wants to re-enter the U.S. You should consult with an experienced immigration attorney to discuss the specifics of your case.
While written by an attorney who is a Florida Bar Certified Specialist in Immigration and Nationality Law, the statements herein should not be construed as legal advice. No attorney/client relationship has been created without a formal consultation with the attorney and the attorney has agreed to accept your case.