After the latest update Safe Assign is no longer available as a separate option instead an originality check is now one of the options for the normal Assignment. This means that you will always see the Assignment icon when you have to submit an assignment instead of the Safe Assign icon.
N.B.: Make sure to click on Submit to submit your paper. You will receive a message: This assignment is complete. Review the submission history.
When you click on Save as Draft you will not submit your paper. You will receive a message: Paper has been saved. When you have saved your paper as draft you can return later to the assignment and submit it by clicking on Continue and then on Submit.
See also Blackboard help