Hi @LondonNicol ...
For questions like yours, you'll need to reach out to your school's Canvas adminsitrator(s) or Online Learning / eLearning / Distance Education department. They would be the ones to help you figure out how you can remove old courses from your Canvas profile. They may have a policy already established for all students as to how and when classes might be removed.
One thing you can do is go to your "Courses" >> "All Courses" screen in Canvas. If you have any courses with a yellow star next to the course name, you can remove that star by clicking on it, and that will remove the course from your Canvas Dashboard (but it will keep it in your "All Courses" list). You can only mark courses with a yellow star if they are active courses...meaning that they are in a current semester.
Hopefully you'll be able to have a conversation with someone at your school soon to find out if you can remove courses from your Canvas profile. Good luck to you!