Perhaps religious/cultural attitudes play a part? That wouldn't account for Utah though.
"The preponderance of current evidence indicates that gun availability is a risk factor for youth suicide in the United States. The evidence that gun availability increases the suicide rates of adults is credible, but is currently less compelling." [1]
There's a lot of good additional data in the original report. According to the table on page 40 [2], self-harm by firearm represented 19,392 of 38,364 suicides. This dwarfed the number of gun-related homicides which was 11,078.
Page 83 explores death by intent. Interestingly, there's also a category for legal intervention/war which represented 344 of all firearm deaths.
[1] http://www.hsph.harvard.edu/hicrc/firearms-research/gun-owne...
[1] - [http://www.suicidology.org/c/document_library/get_file?folde...]
[2] - http://www.cdc.gov/violenceprevention/suicide/statistics/cas...
http://www.npr.org/2013/03/19/174761612/a-turning-point-for-...
Most of the intermountain west is very arid, so rather than "farming" as that is usually understood, the occupation tends to be ranching (keeping cattle).
About the leading causes of death, they tend to correlate strongly with poverty, and it's not surprising to find high rates in poorer rather than richer states.