Doesn't look like there's a way to single out the Desktop via the 'Manage Storage' GUI.
However, you can always just symlink any directory from your iCloud drive; that way you can ensure that only the Desktop folder is being synced. This is with the caveat that while your Desktop files are being stored in iCloud, they're still taking up space on your HD before, during, and after sync. If you do it on every Mac then you'll keep your Desktop in sync between them all (files added, deleted, changed etc); this might not be what you're after though.
If symlinking isn't something you know how to do, instructions are below.
Backup (via TimeMachine or whatever you use).
Then fire up Terminal and run the following to move your Desktop folder into your iCloud Drive:
mv ~/Desktop /Users/<yourusername>/Library/Mobile\ Documents/com~apple~CloudDocs/
Then just symlink it to the usual 'Desktop' location:
ln -s /Users/<yourusername>/Library/Mobile\ Documents/com~apple~CloudDocs/Desktop /Users/<yourusername>/Desktop
Now anything that you add to ~/Desktop (by dropping things onto your desktop etc) will actually be dropped into your iCloud drive. They are of course still taking up local space on your machine. When you delete something from your desktop then it's gone from the 'Cloud' as well. The benefits of this are more for sync between machines (+ access via your iPhone of course).
If you've got another mac, move anything you value from it's desktop folder into your iCloud Drive 'Desktop' folder first, then delete ~/Desktop on that machine and symlink again as above.
As Andreas mentioned in his answer, brctl evict
purges the files. But for me, it seems to work permanently. Even purges recursively through folders. Maybe it is because I purged 40GB of data, hard for iCloud to reset in a heartbeat
>brctl evict SuperBigNestedFolder
evicted content of 'SuperBigNestedFolder/'
Nice!
BUT, when iCloud evicts the files it also throws away all metadata.
This cripples Spotlight by removing the ability to search for text found inside popular file formats such as word, pdf, pages, keynote, or txt.
Best Answer
You could hold down the option + click on the document folder and drag it to another directory (essentially copying it) and then disable sync, so it does not affect the files you just created. Do the same for the Desktop Folder.
Best if you can copy to an external drive, to avoid any chances of losing the local files, until you resolve the unsync and deletion of said files.