Do you mean that students are submitting a first attempt after you start grading the assignments, or do you mean that students are resubmitting the assignment after you graded their first attempt.
Click on the assignment.
If students are resubmitting assignments after the assignment was due, change "Submission Attempts" to "Limited" and set the "Number of Attempts" to "1."
I assume this assignment was already been due before You graded it. What is the "Until" date set to? I set it to the last date and time I want to students to be able to submit that assignment. If you change the "Until" date and time, nobody will be able to submit the assignment after that. I wait until my "Until" date and time have passed to grade assignments.
I hope this helps!