For a Student or primary instructor to be removed from an instructional (SIS-linked) Canvas course, they must be removed from the course in SIS. If not, they will be re-enrolled overnight as a result of the automatic sync process between SIS and Canvas. The only way to alter Student enrollments in live courses in Canvas is through the SIS process.
Teachers can remove users who they have previously manually added to their courses with non-Student roles through the People page of the course. See the Canvas Instructor Guide How do I remove an enrollment from a course?
If a course Teacher needs to remove an additional role from a user who also has the Student role in a course, additional non-student roles can be removed by deleting the enrollment from the Sections tab of the Settings page of the course (each role that the user has will appear as a separate enrollment in the section). See the Canvas Instructor Guide How do I remove an enrollment from a course section?
All enrollments in courses in other, non-Instructional SIS "instances" of Canvas, such as "Training and Development" and "Continuing Education," can be managed by Teachers via the People page.
If a course is appearing on your dashboard and you would like to remove it, you can "un-favorite" it in your All Courses list to hide it by following the steps available in this guide: Canvas - Removing Courses from Your Dashboard
For more information regarding the sync process between SIS and Canvas, please consult Canvas - Courses Do Not Show Up / My Course is Missing.