Blackboard submissions can not* be edited or deleted by the student, even if the due date has not passed. Students can simulate the ability to edit their submissions by saving a draft instead of submitting the assignment. If the student does not submit the assignment and leaves it as a draft, Blackboard will automatically submit** the attempt when it is due.
*Only the Discussion Forums can be edited if the setting is enabled by instructor's choice.
** Discussion Forums' responses do not auto-submit.
If a student wants to be able to edit their submission before the due date, they have to click Save and Close instead of Submit.
If they check their Gradebook, they will be able to see that the submission is currently saved as a draft.
Once they need to edit or want to submit their attempt, they can go to the assignment again and simply click Continue attempt.