You can't.
There are all sorts of reasons, starting with:
1) Cookies are stored on the client, not the server, so you can't access them with C# code anyway except via the Cookies class.
2) They aren't stored in the same place by all browsers anyway: Chrome for example uses an SQLite database instead of individual files, and holds the DB open and locked while it is running, so you can't even access it directly without closing the browser.
Use the "normal" interface to remove cookies:
if (Request.Cookies["UserId"] != null)
{
Response.Cookies["UserId"].Expires = DateTime.Now.AddDays(-1);
}
Will direct the browser to remove it. What the browser actually does as a result though, it not defined...