Now that's not entirely true - the Arduino chip has specialised hardware which does the SPI without bothering the main processor. But 8MHz is as fast as it will go. 4MHz is the default transmission speed.
8MHz is max speed for SPI master, for slave mode it's 4MHz.
Don't forget that the processor does not only have to shift the bits out it also has to provide the information that should be sent. So if one byte is sent an interrupt happens and the next byte has to be written to the SPI register. The interrupt needs several clock cycles so at 4MHz you have no time for any calculations you can only send simple informations.
The Due is not able to be an SPI slave to my knowledge.