When you’re editing the Smart Group criteria, hold your Option key and you will see the Plus turn to an ellipses (…). Although, it’s odd you can a another Kind as a sub criterion.
A smart group such as the following will exclude any item (a document, a group) that has a particular tag. (Ignore the “Date Added” predicate - it’s just an example group.)
I’m afraid I don’t use the tagging feature (A bit too onerous for me. Used to use it but got ridiculously hard keeping track of my tags, and the tag hierarchy. Decided to use Groups instead.).
Is it possible to exclude a group on its own without a tag?
Here’s the only way I know how to do this currently-there may be a better way. Select the contents of the group that you want to exclude (command-a), show info for the selection (command-shift-i), and click on the box Exclude from… Search. Now all the selected documents will be excluded from a smart group search. It should also go without saying that the documents will be excluded from all other searches as well, so use this command carefully.
Also note that selecting the group and checking any Exclude from… option will only exclude the group. All documents within the group will be unaffected.