Under-clocking means lowering the clocks. This will slightly lower the voltage required to run it so you could then try to undervolt it which is lowering the voltage below stock. This can lower power consumption, and if it is a laptop CPU, increase battery life. The actual power saved is going to be very small.
Only if you also under volt it. Doing so will use less power so that would save on your power bill, and allow you to use a quieter cooler. Of course, it's much better simply to buy a low power CPU which has been specially binned to run cooler and at lower voltages.
Undervolting it beneath stock voltages and underclocking beneath stock clocks will haev negligible effects. You're gonna shave maybe 5-10watts off your power consumption which translates into maybe a couple cents off your power bill.
Is that worth having your computer run slower? I think not...
Your CPU will do this anyway on its own. Both varieties, AMD and Intel have speed stepping functions which drastically "underclock" your processor when your PC is idle or doing menial tasks. When demand is placed, the processor ramps up to provide power as needed