The answer would be yes, you can, but i would not advise, mainly because you will never be able to add more stuff to your system. If you have the money to buy a new PSU everytime you change up your system, why not buy a modular?
But anyway, you should be able to just cut the wires, MAKE SHURE THE PSU IS UNPLUGED!!!!!! After you cut it isolate all of the wires so that none of them touch, if they touch they could short out your entire system, or a the very least fry your PSU. Wraping each individual wire in eletrical tape would be a cheap fix, but i would suggest you find a better way to isolate the wires. As long as the wires dont touch you should be fine.