What part of our public school system is failing those children deemed mentally ill?

While browsing in the local category of The Dallas Morning News online, I came across the story of a young boy failing to adjust to society. Not just any teenager having trouble fitting in, but a Hurricane Katrina refugee living with his mother in the Texas town of Tyler. What drew my eye was this headline:
Student held in Tyler teacher's stabbing had long history of mental illness.
Upon further reading, I found out this boy had:
A) A diagnosis of schizophrenia, psychotic episodes and probable mental retardation.
B) A track record of being in mental hospitals in Texas and Louisiana.
C) A past stay in a Smith County juvenile lockup and then in a Texas juvenile prison for stabbing his sister.
D) Family history of mental illness, namely his uncle who brutally murdered his grandma.
and most importantly a discharge from TYC, the Texas Youth Commission, for being more of a burden than they could handle.

Now what is a mother left to do? Home with a son with a disturbed mental state, in addition to trying to support 3 other kids in a single parent household, she has no other option but to put her troubled kid into the public school system. According to state laws, every kid must be accepted into the system, no matter the needs the child has. Here he could not properly be handled as any other special needs student. He had violent tendencies and even had trouble walking in the hallway with other students. It was in this public school, Tyler High, where he fatally stabbed his teacher Todd Henry. Who is to blame here? The Texas Youth Commission for dismissing him when he was not suitable to be dismissed, or the mother for putting him in school? Mind you, his mother had taken him to many a psychiatric hospital and gotten the same diagnosis. Her child was too unstable for them to handle. Then theres the state law that kids must be in school. Therefore, I see her as left with no choice but to enroll her child in high school, despite his dark past. Byron's court-appointed lawyer, James Huggler even said that he was "Absolutely amazed that he was released from TYC, given his mental state and the fact that he was apparently kept in isolation with no effective treatment and no effective after-care program for his return home". He insisted that treatment is what his client needs rather than punishment. I'm thinking Huggler might be right here. His past hospital stays and reformative juevenial center sentences were less than effective. For future cases, troubled teens like Byron need to be properly accounted for in the public school system. Its a tragic instance that a teacher was killed before this was realized.