Congrats on finding a similar plot produced elsewhere by somebody else ... I'm gratified to see that they are essentially identical.
Even the sources and years of the sources identical. But go ahead, claim you independently found the same sources and devised your own graph that just happened to be identical to the Mother Jones article from the exact same sources from the exact same dates. Coincidence???
Details (suicide, murder, ...) are less important to me than the aggregated totals. Guns are a public health problem, not mainly a crime problem. Causing any and all of those deaths to decline is a worthy goal. NRA always frames this as exclusively a crime problem; it is not.
And there is the problem. To lump justifiable homicides (situations where people protected themselves or someone else by using a firearm and killed a perpetrator of a crime) into the catch all "gun deaths" and to try to use the aggregate of gun deaths to make a political case is absurd. Justifiable homicides by firearms actually prove that guns are a benefit to society. Gun deaths from suicides are also suspect. There are other countries that have very strict gun laws and have a much lower gun ownership rate yet have higher suicide rates. If there was a correlation between suicides and gun ownership than we would expect countries with strict gun laws and low ownership of guns to have low suicide rates.
We do not.
There is no relation between suicide rate and gun ownership rates around the world. According to the 2016 World Health Statistics report (link is external), (2) suicide rates in the four countries cited as having restrictive gun control laws have suicide rates that are comparable to that in the U. S.: Australia, 11.6, Canada, 11.4, France, 15.8, UK, 7.0, and USA 13.7 suicides/100,000. By comparison, Japan has among the highest suicide rates in the world, 23.1/100,000, but gun ownership is extremely rare, 0.6 guns/100 people.
Suicide is a mental health issue. If guns are not available other means are used. Poisoning, in fact, is the most common method of suicide for U. S. females according to the Washington Post (34 % of suicides), and suffocation the second most common method for males (27%).
Secondly, gun ownership rates in France and Canada are not low, as is implied in the Post article. The rate of gun ownership in the U. S. is indeed high at 88.8 guns/100 residents, but gun ownership rates are also among the world’s highest in the other countries cited. Gun ownership rates in these countries are are as follows: Australia, 15, Canada, 30.8, France, 31.2, and UK 6.2 per 100 residents. (3 (link is external),4 (link is external)) Gun ownership rates in Saudia Arabia are comparable to that in Canada and France, with 37.8 guns per 100 Saudi residents, yet the lowest suicide rate in the world is in Saudia Arabia (0.3 suicides per 100,000).
Third, recent statistics in the state of Florida (link is external) show that nearly one third of the guns used in suicides are obtained illegally, putting these firearm deaths beyond control through gun laws.(5)
Fourth, the primary factors affecting suicide rates are personal stresses, cultural, economic, religious factors and demographics. According to the WHO statistics, the highest rates of suicide in the world are in the Republic of Korea, with 36.8 suicides per 100,000, but India, Japan, Russia, and Hungary all have rates above 20 per 100,000; roughly twice as high as the U.S. and the four countries that are the basis for the Post’s calculation that gun control would reduce U.S. suicide rates by 20 to 38 percent. Lebanon, Oman, and Iraq all have suicide rates below 1.1 per 100,000 people--less than 1/10 the suicide rate in the U. S., and Afghanistan, Algeria, Jamaica, Haiti, and Egypt have low suicide rates that are below 4 per 100,000 in contrast to 13.7 suicides/100,000 in the U. S.
https://www.psychologytoday.com/us/blog/the-new-brain/201607/fact-check-gun-control-and-suicideYour comparative Japan/US suicide rates are misleading for several reasons. They are wrong or out of date, the difference rapidly declining. They are not age adjusted; suicide is strongly correlated with age and Japan has a markedly older population. Age-adjusted 2015 comparison is Japan=15, US=13, not that dissimlar and the gap has narrowed further in the last 3 years.
Now your just splitting hairs. Gun ownership in the US is 88.8/100 residents and in Japan .06/ 100 residents. Even adjusted for age (or if you need to by gender, height, weight, left-handed or right-handed or whatever other adjustment you feel you need to make to make it more fair) there is a remarkable difference in the availability of guns between the two countries and yet the suicide rate in Japan is higher, as is the case in many other countries that have low gun ownership rates.
Any "need" to defend oneself is hugely greater in the US because, insanely, we have scattered guns by the hundreds of millions everywhere without control. More guns = more death.
Wrong again.

Cherry-picking individual states that depart from a straight line on my graph is meaningless and dishonest. .
But that is not what I did, I used several states as an example (and I stated "as an example") that homicide by gun rates by state are meaningless due to the inclusion of justified homicide and suicide. If you look at the homicide rates by state you have this:

This graph pretty much shows that there is no correlation between murders and gun ownership.
So once you take away suicides, which have no correlation to gun ownership, Your are left with justifiable homicide, homicide and accidental death. Justifiable homicide should not be used as a justification against gun ownership unless you believe people should not be able to legally protect their families and themselves. Homicides have no correlation to gun ownership (see graph above). Pretty much all you have left is accidental deaths and that is really pretty insignificant.

If you are truly concerned about public health concerns, there are many more prevalent issues than guns that should be addressed.

But than we know the liberal cry of guns being a public health concern is really just a charade,