Stop files from being stored on iCloud on Mac mini

That depends on how they are getting stored there.

Normally you would need to either manually move them to the iCloud Drive folder in Finder or turn on the Desktop & Documents option in the iCloud Drive settings for that to happen.

If you are manually storing them in iCloud, then stop and store them in a folder outside of iCloud Drive.

If you turned on the Desktop & Documents option, (it does not turn on on its own) then you can go and turn it off in System Settings ➜ Apple Account ➜ iCloud ➜ Drive ➜ Desktop & Documents Folders.

Beyond that, you would need to explain how they are getting to iCloud or why you think this is happening.

click here ➜ Add your Desktop and Documents files to iCloud Drive - Apple Support

See this article.

Turn off Desktop & Documents Folders on your Mac - Apple Support

This may also help.

Store files in iCloud Drive on Mac - Apple Support

tcarder wrote: … Okay, I tried going to Desktop & Documents Folders and turning it off. Then got a notice that states "If you continue, items will be removed from the Desktop and the Documents folder on this Mac and will remain available in iCloud Drive" plus "New items added to your Desktop or your Documents folder on this Mac will no longer be stored in iCloud Drive." Can you tell me what they mean? I do NOT want any of the files taken off my SSD/Finder!

And if turning off Desktop & Documents Folders stops dumping my files in the iCloud and does not delete my SSD/Finder files, what do I do with the Finder files that already have the cloud on the end of the file name? Will they disappear if I turn off Desktop & Documents Folders?

Remember that iCloud must be prepared for us to be sharing our stuff with our other connected devices. When we turn off D&D in iCloud, new Desktop and Documents folders appear in our User's folder, and those work like we expect from D&D folders, but they're empty! They are empty, because the Mac couldn’t be sure which files we wanted to appear there, and which files we might want to continue sharing with our other devices. So we need to drag the contents of the iCloud Desktop folder to the User's Desktop folder, and they will disappear from iCloud and begin showing up on our computer's Desktop:

Since Dragging from one folder to another on a Mac does a Move rather than a Copy, those files will no longer be available to other connected devices through iCloud. Changes to your Desktop will not be mirrored on your local iCloud Drive Desktop folder or to iCloud.com. 

from:

Turning off Desktop & Documents from iCloud Drive - Apple Community

The cloud with an exclamation mark means that the file was unable to upload / sync to iCloud, so in effect it means the opposite of what you assumed. It still on your SDD and was not possible to sync it.

With that said, if you do have Desktop & Documents turned on then yes, by default everything in those folders is synced to iCloud.

Not sure why you turned it on, again it cannot turn on, on its own, if you did not want this though.

In any case, yes, if you turn it off, it will remove anything it synced from those folders, so move the files out to another folder that is not either of those 2, and then turn it off.