Yes, you should mow your lawn before applying Milorganite to get the best results. When the grass is short, the fertilizer reaches into the soil easily, where the nutrients are quickly absorbed.  On the other hand, long grasses trap some of the Milorganite as you apply it on the lawn. And there's a high chance that rain or water will wash off the fertilizer from the grass.  While you need to keep the grass short, it doesn't mean you have to cut it too low. Just mow the lawn to a standard height before applying Milorganite to it.