Session_destroy() does not only destroy the data associated with the current session_id (i.e. the file if you use the default session save handler), but also the session itself: if you call session_destroy() and then session_regenerate_id(), it will return false, and session_id() won't return anything. In order to manipulate a session after destroying it, you need to restart it.
So in fact, the code mentionned by chris won't work. If you want to destroy the file associated with the old session_id, try the following:
$old_sessid = session_id();
$new_sessid = session_id();
$old_session = $_SESSION;
$_SESSION = $old_session;
Note: this technique will send 3 Set-Cookie headers (one on each session_start() and one on session_regenerate_id()). I don't think this is a problem, but if it appears to be one, you could either leave it alone and wait for the garbage collector to catch the file associated with the old session, or try to delete the file with unlink().