automated by script or manual?
You can select copy from the Tables tab in Manage | Database to copy and paste a table,but this cannot be scripted.
Import records can be scripted and "new table" is an option you can select for the target table. This will duplicate the table and the data in the source table's found set. Though I've never tried if from a script.
It's simpler to back up the entire file or to export the data to a csv, tab or merge file to back up the data.
I wonder why Copy a Table doesn't prompt the user to copy just the structure or the structure and records?
I can tell you "what" but not "why". It copies the table definition, not the data.