Couple of points:

1) There is an wwnership vs requlations debate, how do states with high ownership and low requlations do, when compared to states with high ownership and high requlations.

2) Suicide rate should not be excluded but still considered differently, guns make suicide more appealing due to the easy, quick, and seemingly painless nature of it. However, you need to ban all guns for this to even mitgated, which most Americans find exterme.

3) You need to consider if the firearm mortality rate is a substitue for other form of crimes, example: instead of having 10 per capita gun mortality rate, and 10 per capita knife mortality rate, a state has a 20 per capita gun death rate. Although I have no evidence or data for this, but I'm not making any claims.

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Overall, guns obviosuly allow more opportunity for homicide, suicide, accidental deaths, and escalations, and it makes sense that states with higher ownership would have higher mortality rates due to guns.