To backup a database, you can right click on the project in the project manager and select Export Database. This will create a Sqlite copy of your MySQL database in the location of your choosing. Keep in mind that this could take a while for large databases. To delete the project, right click on the project in the project manager and select Delete. This will mark the database as deleted. The next time you start up Cortex, it will actually delete the database from the MySql server. Deleting a project also deletes all the directories containing render XML files etc. on disk.
If you are using a SQlite database, we create a trash folder and move the project database file into it. This will keep the project from showing up in the project manager. If you want to really get rid of the database, you will have to delete it from the trash folder.