There is, of course, much more to the story of Joseph Mitchell's life than is included here. Please contact me if you are interested in more information.
The following is an image of Joseph Mitchell's Death Certificate from the Historical Records Search section of familysearch.org:
The informant listed on the death certificate, Elizabeth B. Mitchell, is Joseph's daughter. She would have been directly involved with much of the information on the certificate, which gives more credibility to this source of information. Although she was not directly involved, or even alive, for his birth, the information listed on the death certificate is confirmed by the personal history that Joseph wrote about himself. To my knowledge, a birth record in Scotland has not been obtained. Locating a civil registration certificate or a church record documenting his birth would be the best way to verify this birth information.