@jeneen_hill
The format of the SIS CSV files is explained in the API documentation.
Look under the courses.csv section. You need the course_id, short_name, long_name, and status.
Changing the status to "deleted" will remove it from Canvas.
After you have the CSV file created and saved (what you name it doesn't matter, but I typically match Canvas' naming, so "courses.csv"), you go to the Admin page for your Canvas institution and then choose SIS Import. Choose your CSV file and then click process data.
If your Student Information System is aware of which courses need deleted, you could pull the information from there in the needed format. If you want to do it yourself, then I would generate either a Provisioning or SIS Export report under Admin > Settings > Reports. The Provisioning report includes all courses, even if they weren't created by a SIS import, but then you won't be able to delete those through a SIS import, so I would recommend the SIS Export report. What you need to select before you run the report is the "Courses CSV". The report runs in the background and can take a while depending on how many courses you have. You will get an email when it's done.
Download the CSV file that was generated and open it in a spreadsheet (Excel). For the courses that need deleted, change the status to "deleted". Although this can be sent back to Canvas as is, I would sort by status and then delete any rows that were not changing the status. I would also delete any columns that weren't required, but that's not necessary. Save the file (it's already a CSV file if you want to overwrite the download) or give it a new name and make sure it's a CSV.
Then go through the SIS Import process I described earlier.