How do keep my sent messages not being saved in my outbox?

Sent messages are not saved in your outbox. They are saved in the sent message folder. If you do not want them saved. Then open the sent message folder and look for options. One of the options will give you the choice of saving all your sent messages in the aforementioned folder or not saving the messages. If you click the do not save option, you may still have to delete the messages that are currently in that folder but no new ones will be saved.