Backing up Mac mini

If you are using Time Machine to do the backup, it would be to an external drive as that is the only option. See: Back up your Mac with Time Machine - Apple Support

Also note that Apple offers iCloud Backup for iPhones and iPads but not for Mac computers.

It is possible to sync data from a Mac to iCloud if you turn on those options (e.g., iCloud Photos, iCloud Drive including the Desktop & Documents option). Syncing has some of the benefits of a backup (and the benefit of being offsite) but is not the same as a backup. Major differences include the fact that not everything on your Mac can be synced and the fact that if you delete something, accidentally or otherwise, there is only a limited time period (30 days in most cases) during which it can be recovered.

Also see: How to back up your Mac - Official Apple Support

And more information on syncing in:

Set up and use iCloud Photos - Apple Support

and

Access and manage your files in iCloud Drive - Apple Support

and

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