What's the orientation of the mud patch? sun coverage? wind exposure? slope? Is it mud all the time or does it dry and become mud only from heavy rain? What is the composition - red clay mud or dark, top soil mud?

Grass will grow on a vertical wall if the conditions are favorable, so the fact that it slopes shouldn't be an issue. If there isn't enough sunshine then maybe put in a set of steps? Photos always help people understand your situation better.

If it is bare mud due to water flow, try making a leveled raised garden with landscape stones.