Of course! The search form is very powerful. Have you had a look at the search tips (link in upper right corner of search form)? There are lots of filtering tips there.
For your example, all you have to type is clogs -slippers
You could also filter out products based on multiple keywords like this: clogs -slippers|sandals|flipflops
That will search for clogs that do not contain the word slippers or sandals or flipflops.
Here's an OLD video going into advanced search in more depth: http://www.datafeedr.com/videos-sing...earch#videotop