You seem to have been misinformed about what statute of limitations means. That deals with how long the state has to accuse you of a crime after it has been committed. For misdemeanors it is two years. After conviction, an offense doesn't ever come off your record.
The statute of limitations (how long the State has to initiate criminal charges from the date the crime was committed) is 2 years. Convictions stay on your record forever unless it is a first offender case.