The Automator in OSX allows you to create processes, services, folder actions etc. Once you have created a service in Automator there doesn’t appear to be a way to delete it in the Automater app.
Delete an Automator Service
To delete an automator service, open up the finder and navigate your way to you own Library then Services folder. The files are there with the name you gave it in automater. If the file extension is visible it will be “.workflow”.
So for example, if you created a service to hide dot files and had called it “Hide dot files” then it would show as “Hide dot files.workflow”.