Spotlight is a great tool it will index everything, However if you have a Time Machine drive connected to it, there is not point in indexing that drive, or getting your Mac to spend the resources searching through the drive for new files. Therefore, we can stop Spotlight from indexing the drive. This tip, however, will still allow you to search through Time Machine backups, it just won’t search for any other files.
Stop The Time Machine Index
To stop the indexing of a Time Machine drive open System Preferences and select the Spotlight preference pane. Within this pane select the Privacy tab.
When this tab is open drag and drop the Time Machine backup disk into the list.
Its that simple. All of the data from the Time Machine drive regarding a Spotlight index will be cleared. Now every time you turn on your Time Machine drive, it will not try and find and index the files on it. This tip will , however, still index the backups. This is used for building the spotlight index when you go back in time.