Begin by clicking on the "Course Admin" tab in the blue course Navbar

Next click on "Manage Dates" under Site Resources. 

Click on the box under "Apply Filter" to select all content items in the course, then click "Bulk Edit Dates"

Check the box next to "Due Dates, Start Dates," and "End Dates." Then click on the "Set" dropdown and click on "Remove." Click on the blue "Save" button.

You can also quickly get rid of dates with the Manage Dates tool by clicking the "X" or trash icon next to a start/end date or due date