Can I drive this relay shield with an Arduino Due?
You'd have to remove the yellow jumper. Connect 3.3v to the VCC and 5v to the JDVCC. But please double check that JDVCC is connected to one side of all the relays.

This way the opto-couplers are activated by 3.3v signals, which in turn activate the transistor (5v) used to engage the relay.