According to the following image it is possible to use a second SPI bus on the Arduino Due by using Serial1 and SCL1 as SCK0 for SPI (or Serial2 and SCK1).
However I did not find the code necessary to set up the additional SPI interfaces. I would prefer using these SPI interfaces as they are accessible on the stacking headers in contrast to the default SPI.
Additionally can a SD-Card be accessed using these SPI buses while still using the corresponding Arduino Library?
I think the information you are looking for can be found at https://www.arduino.cc/en/Reference/DueExtendedSPI
There are two other alternatives that I can see: if your device supports slave select (which I think they are supposed to), then you can use a different pin to select either device 1 or device 2 (or 3...).
The other options is that if you can connect the clock to only one slave at a time (again, with another pin), you should get the same result - you should be able to use a MOSFET between the Arduino's clock-out and the slave's clock-in, and hook the MOSFET's gate to a spare pin; repeat the procedure, using a separate MOSFET, connected to a different spare pin, to the second slave; then bring one or the other "spare pin" high, to select which way the clock goes. If a slave does not receive a clock, it will not listen for incoming signal. This last one I dreamed up; I don't know if it will work.
