How to use remote Mac Mini without local monitor able to see?
You'll need to purchase Apple Remote Desktop from the Mac App Store.  Once you have it downloaded and installed you can click on the "Curtain" button and that will allow you to VNC or screen share to the system, but anyone physically there won't be able to see what you are doing.


Alternatively, you could click the "Control" button and you'll be asked if you want to login to a new screen sharing session where either you Share the screen with someone physically there OR you are logging in as that user, but to a new viewing session only you can see.