Icreated a group for a field in my 1st data source called 'Dept Specialty' and want to apply same group to the same field in another data source. I tried copying and pasting the grouped field to the other data source, but keeps copying to old data source?

Groups are quick to setup but have a lot of limitations. You can make your own groups using calculated fields which don't have any limitations and can be copied and changed easily. Traditionally you would use a CASE statement but now Tableau supports the IN operator which I don't think most people know about. For example: