You should use a regular expression to extract the relevant part of your string and then apply PHP date functions to it:
$str = "Sun Jun 29 2014 08:00:00 GMT+0800 (Malay Peninsula Standard Time)";
$pat = "/(?:Sun|Mon|Tue|Wed|Thu|Fri|Sat) (?:Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec) (?:0?[1-9]|[1-2][0-9]|3[0-1]) [0-9]{4} [0-9]{2}:[0-9]{2}:[0-9]{2} GMT\\+[0-9]{4}/";
$date = preg_match($pat, $str, $mat) ? date("Y-m-d", strtotime($mat[0])) : "";