Automated Backup with exception of one directory?

You can use TAR to put backup platform independent in archive:

tar -cvpzf backup.tar.gz --exclude=FolderToExclude --one-file-system folderToBackup

Or use RSYNC as it listed above with same key --exclude=FolderToExclude.

Or you can even combine and do rsync into archive (with remote authentication via SSH Key):

Or use restic: