First, you use the tag search
to find all species tags that aren't tatzlpony: category:species, -tatzlpony
Then you take that list of (as of this moment) 1522 tags, go to regular image search and build a query searching for tatzlpony, excluding all other species tags:
tatzlpony, -pony, -unicorn, -anthro, -pegasus, -alicorn, -earth pony, -human, -dragon, …, -tirtouga
In other words, tag categories can only be used for tag searching.
And even if they were available for image search, these kinds of "one, but exclude all others" queries seldom work in any other way than manually listing everything. Since tatzlpony is a species, something like
would also end up excluding tatzlpony and always result in an empty set.