You can open Terminal but navigating to Applications->Utilities in Finder. Or, you can type cmd + spacebar which will open Spotlight. Then, search for Terminal.
There is a handy feature on your mac called tmutil that stands for Time Machine Utility. To disable the local backups, in Terminal type: tmutil disablelocal and you should see your local backups are gone.
In order to read more about tmutil open Terminal and type: man tmutil which will open the manual for tmutil. Here you can find out to restore local backups if you'd like.