If you have a drive power cable splitter, you don't have to cut your power supply cable. If you don't have one of these splitters, you can still make these connections by working directly with the power supply cable - not as easy or convenient but possible.
Typical power cable splitter
Here's a rough diagram of what I'm making.
Here's the one I'm using now.
Not pretty but effective.
Here it is connected to two old hard drives.
Here it is with two drives and a power supply connected.
Notice that I protect the drive circuit boards with a non-conductive cover.
Here's a closer look at the connectors and the DPDT toggle switch.
Warning: be aware that the sensitive electronic components of your computer can be easily damaged (destroyed!) by static electricity from your fingers, tools, or by coming in contact with any other material that may be charged with static electricity. Discharge yourself and equipment by touching the metal case of your computer or a grounded appliance or device before handling sensitive circuit components, then use the utmost care.
Warning: before making this switching circuit, look at your hard drive while it is plugged into your power supply. See how the red wire is to the inside of the socket and the yellow wire is to the outside of the socket. The inside red wire is 5 Volts DC and the outside yellow wire is 12 Volts DC. The black wires are grounds.
Regardless of the color of the additional wires that you may use, if you swap the position of the 5 Volt and 12 Volt inputs to your hard drive, you will instantly destroy the hard drive when you turn the power on. That also applies to the black ground wires. If you swap a ground wire with either the 5 Volt or 12 Volt inputs to the hard drive you will instantly destroy your hard drive when you turn the power on.
It is best to check you new wires with a multimeter to make certain your wires connect the correct voltages to the hard drive before plugging the connector into the hard drive. If you get them wrong, your hard drive will instantly die when you turn the power on.