Mac Mini machines made before July 20, 2011 have an internal CD/DVD drive. Models made after this date do not include an optical drive. In some rare cases, a disc may become stuck in the machine and it may not eject with the standard methods. The standard methods to eject discs are to press the Eject button on the Mac keyboard, or drag and drop the desktop icon for the CD/DVD in the drive to the Trash Can or click the "Eject" icon next to the disc in the Finder window. If these methods fail, other steps may be required.
Going Beyond Standard Eject Methods
Sometimes a simple solution is the best solution. Sometimes dust or other debris collects on the rubber seal and it may prevent the disc from ejecting. Use your finger or some other soft tool to quickly clean or clear the opening of the drive and attempt to eject. If that fails, there a few utilities you can install, such as DiskUtility, Toast Titanium or CleanGenius. Each of these may resolve a stuck eject command. You can also power down your Mac for awhile then reboot and try again. Failing that, you can restart the computer while holding down the "Option" key. Let go of the Option key and press the "Eject" button on the keyboard when the startup disc selection screen appears.