It can be done via a url with the without_term_id / without_term_value_id parameters. The Identify Dialog also provides an interface for this (in the “More Filters” section).
If other parts of the iNat interface don’t currently provide the necessary options, I would suggest you make a feature request. There’s a recent forum thread asking for ideas for a revamped Explore/Observations Search Page, so that might be a good place to discuss issues like this.