To exclude certain taxonomic groups, append the string &without_taxon_id=X,Y,Z to the URL, where X,Y,Z etc are the ID numbers for each taxon you want to exclude. For example, this URL is a search for Australian observations, but excluding ray-finned fishes and sharks + rays:
https://www.inaturalist.org/observations?place_id=6744&without_taxon_id=47178,47273