Multi master SPI mode? Or any intelligent way to switch only time between two masters?
The main problem here is probably not to pick a suitable MUX - most analog switches will probably work. But rather how to sync "GPU" and "MCU". Because MCU should be speaking most of the time, except when GPU takes over, then it should be quiet.

The GPU can't just cut the SPI wires when it pleases, because then it will corrupt an on-going SPI transfer. This can have very bad side effects if the MCU is interrupted when writing commands to the display.

You can solve this by having the two devices listen to each others /SS lines and use that as a means of "arbitration". 

GPU:  


When /SS line out from MCU is pulled low, remain quiet during the on-going transmission. 
When /SS from MCU goes high, grab the bus by starting a SPI transfer and thereby pulling /SS from GPU low.


MCU:


Before starting a SPI transmission, check /SS line from GPU.
If /SS line from GPU is high, we may send.
If /SS line from GPU is low, go passive/sleep for a certain amount of time, before checking again.


MUX:  


Wire it so that the two different /SS lines are used as channel select, determining the source of MOSI and CLK. (MISO shouldn't be needed for most displays.) Either by finding a suitable switch or by inverting the signal of one of the masters through BJTs or similar. 
You can perhaps make the MCU /SS recessive by connecting it through a 10k pull resistor, so that the GPU /SS can override it without having two outputs competing. I suppose there are lots of ways to solve this.