Hi Vercuh,
If you're unable to quit Mail normally, try forcing it to quit from the Apple menu bar. Select the Apple in the menu bar, then Force Quit. From there, select Mail. It should force the program to quit, after which you can restart or shut down your Mac.
If this becomes a recurrent problem however, do you see any other info regarding Mail when trying to quit it? For example, "Mail was unable to quit because of..." and then it lists a reason?
You can also see tips on what to do if an app is non-responsive here:
When an app on your Mac stops working, try these suggestions.
- If an app doesn’t quit as expected, or it’s unresponsive, you can force quit the app (you may lose unsaved changes). Choose Apple menu
> Force Quit, select the app in the dialog that appears, then click Force Quit. - If the app quit, reopen it by clicking Reopen in the dialog that appears.
- Restart your Mac by choosing Apple menu > Restart.
- Make sure the app is compatible with your version of macOS.
- Open another file in the app. There may be a problem with the original file.
- Check for updates to your software.
- Disconnect any peripheral devices you just connected (for example, a printer). They may not be compatible with your version of macOS.
- Uninstall any app plug-ins or enhancements from other manufacturers.
- If you recently updated the app or macOS, a plug-in or enhancement you installed may no longer be compatible.
- Diagnose problems with your Mac to learn whether hardware you installed, such as additional memory, is incompatible, improperly installed, or defective.
Cheers!