There are several ways to assess assignments:
Note: The grades you manually enter for quizzes, discussions, and assignments grade items are automatically synchronized back to Quizzes, Discussions and Assignments.
The File Submissions area of Assignments has a log that can be filtered to determine if and when a learner submitted a file, and whether the learner or instructor deleted the submission.
Do the following:
On the Assignment page of your course, select the small downward pointing arrow to open a drop down menu. Then, select Submission Log.
Filter the log as applicable, by Submitted (shows all submissions), Deleted, Restored, or Started.
Sort by Date, Event or Submission.