Mind is a function of the body. Certain parts of the brain, to be more specific.
As far as dualism/determinism goes, I think most philosophers favor determinism, but I could be wrong.
There is of course the problem of consciousness, which may be what you're referring to. I believe that the problem states that biochemical reactions and whatnot cannot account for the existence of qualia, or what we experience.
A case for separateness of consciousness is often made by the "zombie" thought experiment, where, as I understand it, you imagine a world where "zombies" go around exactly the way we do, reacting to things, etc, but are not conscious of what they are doing or why they are doing it.
My problem with this is that in order for the zombies to go around exactly the way we do would require that they have the same cognitive functions as any of us, including memory, sensory processing, creativity, logic, and so on. Basically to say it's possible to imagine a world where zombies act exactly the same as people but don't have consciousness assumes that consciousness is something separate to begin with, so I think that makes the argument basically circular reasoning. I could be wrong, though.
There's also the question of whether a computer could be conscious in the same way as a human in that it could experiences qualia. Simply running a program to identify the color red based on wavelengths is not the same as *experiencing* redness the way we do. Our eyes essentially process wavelengths, and our brain identifies it as red, but subjectively when we look at something red, we're experiencing redness. The question this raises (or one of them) is not about the mechanics of visual processing, which a computer could conceivably accomplish, but whether it could experience redness the way we do.
Personally, I think it's likely that the determinists have it right in that the answer will not involve to some separate substance. It seems possible to me that qualia is just the output of how the brain processes information.