The best tool for cutting grass on a slope is not the one that's best for the grass, but the one that's best for your safety. Slipping wheels, tipping decks and treacherous footing contribute to frustration, damaged equipment and accidents. Certain tools are better than others, but removing the grass entirely may be the best solution.
Riding mowers have the weight and power to move up and down a hillside, but those same qualities can work against you. Riding mowers often have a higher center of gravity than standard mowers and may easily tip, even rolling up and over backwards as you travel up a slope. If a riding mower is your only option, don't mow across or directly up a particularly steep grade. Instead, only ride the mower in low gear down the grade and circle back to the top for the next pass. If the wheels slip, stop mowing.
Electric and Manual Mowers
Lightweight mowers are a good choice for a hillside lawn. Electric mowers weigh considerably less than do their gasoline-powered counterparts, making them equally less attractive to gravity's pull. If you aren't thrilled with dragging a cord across the lawn or waiting for a battery to recharge, consider a rotary push mower. These Earth-friendly mowers are lighter than gasoline-powered mowers, but pushing these across a hillside is labor intensive. Their exposed blades are also hazardous to slipping feet.
Most lawn grasses aren't happy growing on a steep slope. Depending on the slope's exposure, the grass often receives too much or too little sunlight. Irrigation water or rainfall travels down the slope. Soil at the top is too dry, while soil at the bottom may be too wet. Consider removing the struggling grass entirely and terracing the slope with trees, shrubs and perennials. If terracing isn't an option, consider growing a tough, adaptable ground cover suited to your climate. As a last resort for rural gardeners, a herd of goats makes excellent lawnmowers.