Make sure the Super Drive is connected directly to the Mac since adapters, docks, hubs will prevent an Apple Super Drive from working (the exception is if you have a USB-C Mac and need to use an Apple USB-C to USB-A Adapter).
Try disconnecting all other external devices.
What type of CD is it? Data, music, video? What type of file format is being used on the CD? macOS cannot handle certain file systems while Windows & Linux may be more forgiving (especially Linux). It all depends on how the CDs you are trying to access were created.
You don't give any details on the exact model of your Mac. If it is an older Mac, then the Super Drive may not be compatible with it. I know some Apple Super Drives will not work certain Macs (I think Apple included a note with our Super Drive years ago specifically mentioning this issue, but gave no details on why although I have seen references on these forums it may be due to some Macs not being able to supply enough power to operate the Super Drive -- nice to know after a purchase was made). Maybe a split "Y" USB cable which uses the second connection to supply more power would help. Personally I would just use a standard USB optical drive or use your other system to transfer the contents from the CD to other media.