1. Most of the gamey-ness comes from the fat. Unlike the pork or beef fat, mutton fat has a strong odor. You could try to trim off as much of it as possible.
http://chestofbooks.com/health/nutrition/Medicinal-Meals/Mutton-Fat.html

  2. It also depends on whether the animal was grain-fed or grass-fed. The latter, although more natural, tend to produce meat that has a strong smell. 

  3. As for cooking mutton, I've found the only satisfactory way of getting rid of the smell is to make a curry out of it. There are many good Indian mutton curry recipes on the web.