Hi, I made a website for this purpose. You can apply negative filters for all the stuff that you can also filter on itch.io. Generally speaking my site is always a bit behind itch.io, and I don't have impressions and views data, so my sort options for popularity aren't as good as the ones on itch.io, but for excluding stuff from your results, it does the job.
https://kalrog.itch.io/better-itch-search
Viewing post in Filters to exclude tags
Oh?
I do not know how your site works under the hood, but on Itch, genres are tags for all intents and purposes.
You can select 1 main genre, and you can select any genre as one of the 10 tags.
In that tag selection box for browsing, that says "Select a tag...", all the genres appear there.
The only difference is, that the url modifier reads "genre-x" instead of "tag-x" and that genres have a shortcut selector interface on the left side. Also, the main genre is shown in the browse section.
Even the undocumented url exclude method treats them the same. The very first example ever given for this is literally
https://itch.io/games?exclude=tg.visual-novel