Observing USB Gamepad with Arduino?
As mentioned, the problem is the gamepad you have uses communicates over USB, which requires a USB Host chip to communicate with. However, USB Host shields can be found on eBay (under "arduino USB Host shield") from US$10, and they come with a USB socket, so you could use it easily with another gamepad that hadn't had the connector snipped. This also would allow use with HID devices such as mice and keyboards if you wished, so a worthwhile shield to own.