When the animals graze, they eat the small plants along with their roots. due to overgrazing their will be nothing to hold the soil which will lead to soil erosion i.e. upper layer of soil will be washed away ,then their will be lackness of humus and no new plant will grow that will lead to desertification.
When the cattle graze then they dig plants from their roots . and hence if there will nothing to hold the soil then soil erosion would be there. even that it would be easy for wind to carry soil particles from one place to other. and then no plant would be there. hence desertification would be there.