To remove cookie from server one need to set its expiry time to current time.
e.g. J2EE container one can remove the cookie in following way
HttpServletResponse response = (HttpServletResponse) servletResponse;
Cookie cookie = new Cookie("cookie-key", "");
//.... set all the other attributes same as that of existing cookie, like path and domain.
cookie.setMaxAge(0);
response.addCookie(cookie);
setting max age of cookie to 0 I am setting its expiry to current machine time.
JavaScript
document.cookie = "username=; expires=Thu, 01 Jan 1970 00:00:00 GMT";
For more details refer