You can certainly select different clocks for processor, memory or whatever, but you need to add a clock crossing adapter between these system sections.
This solution could be convenient if you have one or more devices with a smaller fmax than most of the others.
But Nios and onchip memory are generally able to run at the same clock rate, so I think separate clocks is not the best option. Consider that clock crossing circuitry involves delays, data latencies and resource usage. So, running the whole system with a single clock, could possibly lead to better performance, although you have to use a lower clock frequency.