The only easy way to do that with a USB joystick: unplug it. Normally, they don't have power switches on them to shut them off, and if that one doesn't, the only other way is to unplug it. Even disabling the USB hub in the hardware profile won't stop the hub from giving power to it.
If you don't want to unplug it and the light bothers you that much, cover it with something, hide it under your table, close your eyes, something... but there's no way to do what you want unfortunately.
That's just poor design on their part. Some companies include a feature in their product software or by a hardware switch to change, reduce or turn off lighting (like my Logitech G13 and Sidewinder keyboard), then again, some don't (like my Roccat Apuri).