The majority of Blackboard assignments only allow one attempt for submissions.
The number of submissions and the ability to re-submit an assignment is controlled by the Instructor of a class. If the assignment is set to allow re-submissions, then when you go back to the assignment, a button will appear near the bottom of the screen labeled "Start New Submission."
If that button is not available, you will need to ask your Instructor to clear your attempt. It is suggested you contact your Instructor via email in Blackboard (in the Instructor User Group). Explain you made a mistake and ask he/she to reset your attempts.