For conventional push mowers, mowing on a slope can carry an added risk. Make sure to avoid mowing directly up a landscape slope as the mower blades can fall towards your legs if you fall or lose grip. Sideways is always best. If it has been raining, try to avoid mowing on a slope altogether as the risk of slipping on wet grass is much greater.
For Ride On or Zero Turn mowers, mowing on a landscape slope is different to push mowers, you should mow up/down the landscape slope as this minimises the risk of a dangerous rollover, a roll hoop is available on most zero turn mowers to also reduce the risk.