In this article I will show you to clear cookie in ajax post method call to a controller by setting the cookie expiration date to the past date. When the user request for a page from the domain or path, the browser cookie determines that the cookie expired and removed.  

[HttpPost]
        public JsonResult LogOut()
        {
            HttpContext.Session.Abandon();
            //Delete the authentication ticket and sign out.
            System.Web.Security.FormsAuthentication.SignOut();
            // Clearauthentication cookie.
            HttpCookie cookie = new HttpCookie(System.Web.Security.FormsAuthentication.FormsCookieName, "");
            cookie.Expires = DateTime.Now.AddYears(-1);
           HttpContext.Response.Cookies.Add(cookie);
            return Json(new { RedirectUrl = "/Admin" });
        }

$(function () {

$("#btnlogoff").click(function () {
                $.ajax({
                    type: 'POST',
                    url: '@Url.Action("LogOut", "Home", new { area = "admin" })',
                    data: {},
                    contentType: 'application/json; charset=utf-8',
                    dataType: 'json',
                    success: function (response) {
                        document.location =response.RedirectUrl;
                    },
                    error: function (xhr, ajaxOptions,thrownError) {

                   }
                });
            });      });

Here, the asp.net token based authentication cookie deleted and sign out from the web application and redirect to the sign in page.