You can trash assignments in WebAssign using the Assignment Editor, if you are the assignment author. Note that if the assignment is scheduled to a class for which you do not have access, you cannot trash the assignment.
When you trash an assignment, students can no longer view it if it is scheduled. Alternatively, you can remove a scheduled assignment from your class; doing so removes it from view by your students and removes the assignment scores from your GradeBook and class score views. See Unschedule Assignments.