By default, Time Machine does not back up external drives, but you can change this. Time Machine can back up any locally connected drive, although Apple configures it by default to excludes external drives. You can ensure that external drives are backed up by following these steps:
Open the Time Machine system preference pane.
Click the Options button.
Select any drive in the exclusion list that you want to have Time Machine include.
Click the - (minus) button to remove it. (Repeat for additional drives.)
That’s all you have to do.
How to make sure Time Machine backs up external drives
by Glenn Fleishman, Senior Contributor, Macworld