Watson used 'mind' in the same way that the people who talk about the mind surviving the death of the body use it.

There's no such thing. The computational properties of the brain could be duplicated (generally speaking) in another system, but they would no more survive the destruction of the brain than the seventy-miles-an-hour survives a car crash.

There are many, many reasons to reject Freud. To the degree that Watson and Skinner were trying to make psychology a science, their positions were incompatible with Freud's, who considered his work to be a form of art and despised attempts to make his psychoanalysis part of medicine.