You can only delete an Assignment Type that has not been used. If it is not used you will see trashcan icon. If it is used you will see a Padlock Icon.

In order to remove Assignment Types no longer needed, you must first inactivate the type. To inactivate an Assignment Type navigate to:
  1. From the menu in the to left select Academics
  2. Navigate to Grades > Grading Setup > Assignment Settings
  3. Under Assignment Types click the Editing Pencil next to the Assignment Type you no longer want to be active
  4. Change the Active Yes to No
  5. Click Save

Users will no longer be able to add this assignment type to a new assignment, however inactivating this will not remove any Assignments already added to the Course with that Assignment Type.