Is it possible to exclude queries from search results?

What I’m trying to do

I am searching for a note. I do not want to see matches with queries that match my search term. For instance, I have a note for a person named “John Smith”. In other notes I have queries looking for tasks related to John Smith–“description includes John Smith”. I want the search results to include the notes referencing John Smith but the notes containing the query.

Things I have tried

What do you mean by queries — embedded searches? DataView? Tasks? It would help to post an example. If the query is a single line it will be simpler to exclude, but if not it should till be possible.

Also I think you left out a “not” in the last sentence.