When the "Enable cookies for this web service" is checked, QIE will extract any SET-COOKIE HTTP headers in the response and store these values in a cookie jar. You are correct, that you can manually clear the cookies by clicking the button.
As far as programmatically clearing the cookies, we do not have a call to clear them. You could try adding a blank cookie header in your webservice call. This will override the cookies QIE would have sent. Without sending the expected cookie, the server will likely return new SET-COOKIE headers on the reseponse which would update the internal cookie jar for the web service.
Note below that it will add an entry in the parameterMap of ("http.header.Cookie", " ")

Does that work for you?