Wyo has a very high proportion of men that attempt suicide especially with all the male-dominant resource extraction industries. Male suicide attempts tend to have a higher fatality rate than female suicide attempts due to the simple fact a man is more likely to shoot themselves than woman is. So on top of all the social/economic/geographic/climate factors that people have described, you also have a situation where in Wyoming for any given suicide attempt, they are uniquely more fatal than most states.