Push mowers are better for mowing terraced lawns because they are easy to lift and lower onto the next terrace.
Mow the top section of the hill first, going back and forth across the slope instead of up and down. Turn the mower off when you are done with the first level, and wait for the blades to stop spinning.
Lift the mower up and lower it down to the next terrace. Turn it back on and mow the terrace. Since terraces are flat, you can go back and forth or up and down.
Repeat this with each terrace. Always turn the mower off and wait for the blades to stop turning before you pick up the mower and bring it down to the next terrace.