You must connect SPI to the "SPI header" http://arduino.cc/en/Main/ArduinoBoardDue
. This is the only access to SPI on Due.
SPI: SPI header (ICSP header on other Arduino boards)
These pins support SPI communication using the SPI library. The SPI pins are broken out on the central 6-pin header, which is physically compatible with the Uno, Leonardo and Mega2560. The SPI header can be used only to communicate with other SPI devices, not for programming the SAM3X with the In-Circuit-Serial-Programming technique. The SPI of the Due has also advanced features that can be used with the Extended SPI methods for Due.