If you imported content from last year's course into your current term course you have several options. You could go into the Assignments view of your course (left hand navigation) and delete any assignment that you will not be using this year. You could also edit the assignments individually and edit due and access dates to reflect this year's schedule. You could also go to your calendar, go back to last year and drag and drop assignments into the current term, using the mini cal. Alternatively, you could un-publish your assignments if you want them to disappear from the syllabus, modules, etc but still leave you the option of turning them back on. Please let us know of you'd like more info on any of these strategies or prefer a different solution.
If you do not want the assignments to come over, when you do the course copy, you should select the Select Specific content option. This will allow you to choose which pieces of the course you would like to copy over. At this point you would need to go and un-publish the current assignments to remove them from the syllabus and grade book.