I would not; I would unplug the unit from the wall and disconnect each of the power cables from the devices they power and then thread the power cables back through the case so all of them have cleared the holes, channels, and hardware so I could unscrew the PSU and remove it with the cables intact.
If you must cut the wires, make sure the PSU is not plugged into the wall outlet. Know that PSUs have capacitors that will very likely discharge the current they hold as soon as you cut the wires. Wear heavy rubber, or other insulated gloves, or ask an electrician friend to do it.