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.