Just wondering, How do seriously mentally ill or retarded people advance spiritually ?
Mental disease is a term that covers a broad range of maladies. You might say that we are all a little bit "peculiar" in our own, idiosyncratic way and that the term "mentally ill" is but a definition of degree of "abnormality." All souls can, and do, spiritually "evolve" in the sense of expiating and resolving past karma whether one’s challenges are physical, mental or spiritual. Souls incarnated with mental illnesses or diminished capacities have unique obstacles and should be helped to overcome whatever they face, just as we would help those with physical disabilities.
I understand part of your question to be whether "ill" souls can simultaneously advance toward freedom and ultimate liberation. The answer is "yes" but "progress" may be constrained by the circumstances. If an illness negates one’s free will and the ego’s control of actions/choices, then progress may be limited. Conscious transcendence of ego may not be possible in severe cases where the "body/brain mechanism" is too impaired and subject solely to karmic influences with little ability to influence them. But, I think it fair to say that most mental illness is not to such a degree.
We also mustn’t overlook the ability of a person to act on levels beyond the rational mind. Is a person capable of love, feelings and intuitive insight? On these levels, expansion of sympathy and awareness might flower and lead to significant spiritual growth. The answer to the question of "how" souls evolve is not essentially different for those healthy or ill. Is the sense of "self" expanding beyond the limitations of ego or is it contracting into the firmer grip of limitation and identification with the body, likes/dislikes, and emotions? To achieve freedom, we need a healthy sense of "I" in order to ultimately transcend it, but any movement in a positive direction, however limited, is to our benefit.