There is no standard, universal definition of what constitutes being severely mentally ill. As mental illness
always occurs in a social context, a great deal of what determines severity is the support system and responses of the people who interact with the mentally ill person.
One way of thinking about the severity of the mental illness is to think about how it impacts a person's social functioning. For example, does your son manage to hold down a job? Does he have meaningful personal relationships? Does he have goals for his life? If the answer to these questions are "yes" then this is excellent and suggests that he is less impaired by his psychiatric problems then some others.
For the purposes of governmental programs, although this is not universally true, "severe mental illness" is often reserved specifically to mean those who suffer from psychosis. Psychosis is an altered representation or interpretation of reality. It can have many manifestations, but common ones include hallucinations (such as hearing voices) or delusions (such as believing someone is spying on you). The types of psychiatric conditions that can include psychosis are bipolar disorder
I suggest that the best first step is to have your son discuss his psychiatric problems with his psychiatrist
to determine what programs and therapies might be available for him.