The notion of mind uploading assumes that the mind arises from activity in the brain. This notion is known as "materialism," as opposed to "dualism," which supposes that the mind (or "soul") exists separately from the brain, but connected to it in some fashion. Descartes, for example, believed that the mind communicated with the body through the pineal gland.
The evidence for materialism is overwhelming. Nearly any aspect of the mind -- temperament, memories, appetite, and so on -- can be disrupted by damage to specific areas of the brain. Modern brain imaging techniques can even detect brain activity correlated with thought.
Nonetheless, the question of exactly how consciousness arises from unconscious matter is a nontrivial problem. Some scientists have suggested that consciousness is a fundamental aspect of the universe, and directly related to information processing; others believe it requires a very particular arrangement of neural circuits, resulting as a by-product of our evolutionary history. Clark Dorman has prepared an excellent review of some books on consciousness and the brain.