Green’s Dictionary of Slang

1. (US prison) to complete one’s sentence.

1927		‘Jargon of the Und.’ in DN V 448: Graduate, To be released from prison after having served the sentence.
1949		Monteleone Criminal Sl. (rev. edn).

2. to increase, through knowledge and sophistication, one’s status within the ranks of one’s peers in the streets and the criminal milieu.

1983

R. Klein Jailhouse Jargon and Street Sl. [unpub. ms.].

3. (drugs) to stop using drugs altogether or to progress to stronger drugs.

1971		Illinois Legislative Investigating Committee Drug Crisis in Spears (1986).
2001		ONDCP Street Terms 11: Graduate — Completely stop using drugs; progress to stronger drugs.