You are correct to say that mind and brain are two different things in Buddhism.
However, brain plays a critical role for the working of the mind, as explained in the post: “Brain – Interface between Mind and Body”
Therefore, when the brain function is weakened by schizophrenia, that will affect the mind in the same way that any damage to the brain will affect the mind. In fact, as we get old, brain function deteriorates and that affects the mind too. So, there is nothing special about schizophrenia in that sense.
All those, including schizophrenia, are kamma vipaka, just as cancer or any other ailment is due to kamma vipaka.