You're going to need to use DateTime.ParseExact
:
var date = DateTime.ParseExact(
"Mon Jan 13 2014 00:00:00 GMT+0000 (GMT Standard Time)",
"ddd MMM dd yyyy HH:mm:ss 'GMT'K '(GMT Standard Time)'",
CultureInfo.InvariantCulture);
after parsing the date you can then send it out your way:
date.ToString("yyyy-MM-dd");
Here's an Ideone to prove it.