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
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.
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.
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removed opinion on "most people", changed "goat"to "animal"(since mutton can refer to goat and sheep as per wikipedia)
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