yes, you can do something similar in data assist search, but it will require hand coding, a good knowledge of querystring variables and how to manipulate links.
the key is to make sure that the search is configured to use the GET method instead of the POST method.
using the GET Method, the search parameters are passed using querystring variables
you can create links that clear a querysting variable, but retain the rest. the exact code to do this will depend on how your search is configured, and the querystring variables that it produces