Is there evidence that brain and mind are separate? I've heard countless discussions about whether or not the mind is separate from the brain, but they have all been philosophical. 

I am looking for peer-reviewed studies that suggest the mind is not just a by-product of the brain, as I feel this is quite an extraordinary claim.

Are there any such studies?
Another approach to this issue is to consider whether this kind of reductionism ("mind is just a by-product of the brain") is useful. Strictly speaking, architecture is "just a by-product of physics and materials science", but there are phenomena that are usefully described at the level of architecture and would not be well-captured by the atomic and molecular properties that underlie them. The same holds for the mind and brain: we can study the neural correlates of psychological phenomena and these studies are sure to help us understand those phenomena, but they are not logically equivalent. This view has been articulated by many people, here is one (peer-reviewed) example: Miller, G.A. &amp; Keller, J. (2000). Psychology and Neuroscience: Making Peace. Current Directions in Psychological Science, 9(6), 212-215. You don't need to be a dualist to hold this view, just to understand that phenomena can have different levels of analysis.