The slope is ideal for mowing along the contour - a person walks along the contour and cuts the mowed grass from top to bottom.
Gravity helps - the "empty" scythe rises uphill and the biomass slides down onto the already mowed land. If I'm not going to use the entire shot (a full semi-arc), a shorter mowing area is enough. It is sometimes less physically demanding than mowing on the plain. But when the grass is overgrown, it often lies downhill. Also after heavy rain. Then proceed from top to bottom so that the scythe gets under the lying stalks. For this purpose, it is a good idea to insert a wedge between the scythe and the mowing area, so that the blade does not tend to cut into the dirt, and the mowing area should be longer. That's why I think it's best to buy a snath of the same size as for mowing on a plain.