So Europe has mass killings too. However, deaths by gunshots are much less common over there than they are in the States, and that's more indicative of our gun problem over here. The mass killings are aberrations - and make up a small percentage of deaths by gunshot, so that's a misleading list you gave.
I have a list of my own, more indicative of the dangerous gun culture here, illustrating how Europe has it much better than us. It's a list of countries by firearm-related death rate in a given recent year.
The United States is sandwiched in between the advanced, great nations of the Philippines and Mexico.
Other than Estonia, the U.S. has a significantly higher gunshot-death rate than every other European country on the list. This proves, like it or not, that Europe does a much better job at regulating firearms, making them harder to get for the average joe, etc. Our firearm death rate is more than 10x higher than that of Spain. The easier our country makes it to get a gun, the more gun-related deaths there will be. It's very, very simple, I think. More guns circulating = more deaths. Shutting down mom & pop gun shops that Joe Schmoe can walk into and buy a gun will decrease the amount of firearms in use. Putting more effort into cracking down harder on those who own illegal guns will also go a long way - something the government definitely is capable of.
Sticking with Spain, here is a brief rundown of their policy when it comes to citizen-owned firearms:
+Gun owners must be licensed and undergo strict medical and psychological tests.
+No one is permitted to own more than six hunting rifles and one handgun.
+Firearms must be registered and inspected annually.
+Machine guns and submachine guns are banned, as are imitation pistols.
I understand that guns would still be accessible in America if made illegal - just like they are for some people in Europe. Laws will always be broken to a degree and nothing will ever be perfect. But there's no reason to not move in that direction for the sake of making the U.S. safer. Things would IMMEDIATELY improve by making guns hard to get, like they do in Spain, and tons of other European countries.
And for the record, the Second Amendment is the only Amendment I don't support.