Yes and no. Graduating would imply that a person no longer needs mental health services, and when it comes to mental illness, these are something that often has to be maintained either with medication or counseling or both.
There are many children who grow up in residential treatment centers and you could say they too "graduate" at the end when they reach the age of 18 and enter society all on their own. Whether or not they'd ever return to a hospital, outpatient treatment or another residential setting is hard to say. Some do and others don't either because they're tired and do not believe in the therapeutic process, others are mentally handicapped and can't make the right decisions for themselves and others simply don't care.
I guess your question would depend on your own situation. If you want to switch care providers, that is something you can do for whatever reason, especially if you feel hindered with your current provider.
You can exit any institution freely by simply disconnecting from your provider for whatever reason you see fit. You simply inform them that you are leaving and will not be back. You don't owe a provider anything. Graduating as the expert suggests implies that you are finished or "all better". You may be experiencing less symptoms but eventually you may need care again. It is not graduating as much it is taking a break from whatever care you are receiving. You are not "done" but more in less need than you were months before.
You should end your association with a provider by giving you and even the provider closure. You inform them that you no longer wish to participate in any therapeutic process and leave on good terms so that you can always return when you need to.