Someone on Reddit found a way to include multiple exclusions. For example:
https://itch.io/search?q=Train?exclude[]=tg.horror&exclude[]=tg.adult
EDIT
Finally home from work so I could do a little research. Back in 2017, Leafo implemented a quick fix in response to the post Can I use exclusion filters?. This fix allows users to exclude one tag from the browse page. There is no way to exclude multiple tags.
I also looked into how to exclude tags in Search. I'm no web developer, but from what I can tell you can't exclude tags from your search results. The website just isn't designed to do that.
So https://itch.io/games?exclude=tg.horror will hide all games tagged as "horror, but https://itch.io/search?q=game&exclude=tg.horror will not.