You can remove or hide courses from previous semesters from the My Courses Module. This does not remove the course from Blackboard, but hides it from the My Courses view so that you only see the courses you are teaching for the current semester when you first login to Blackboard.
Click the gear icon in the top right of the My Courses module.
On the Personalize: My Courses page, click the box to the left of the course name to select all of the features, and then click it again to deselect all. Alternatively, click the boxes on the right to choose exactly which features you will see for each course.
Selecting boxes will add to the courses or information that you will be able to see.
You can also choose the order the courses are listed in the module by moving your cursor to the left of the boxes, until it has a crosshair icon and then dragging the course to the desired position.