Wait to mow the steep slope until the grass is completely dry, as moisture from rain or dew increases the odds of slipping.
Put on shoes with thick nonskid treads to prevent slipping when you are on the slope. In addition, test the tire pressure in the mower tires, using a tire gauge to inflate them to the manufacture's suggested pounds per square inch (PSI), if needed.
Place a push mower at the bottom of the slope on the left side. Although some riding mowers can mow slopes, they are for professional landscaping use only and require specialized training.
Start the mower and push it across the slope to the right side. When you reach the end, turn the mower toward the top of the slope and push it up until it's just above the first mowed row. Push it back across the slope to the left side.
Continue mowing in a side-to-side pattern until you reach the top of the slope.