Nah, even the complete unavailability of guns (in a purely hypothetical world) wouldn't stop mass killings--
And guns would still be available.
James D. Wright and Peter Rossi, "Armed and Considered Dangerous", (Aldine 1986, 2nd ed 2008, ISBN-13: 978-0202362427), US NIJ Felon Survey of 1,874 felons in 18 prisons in 10 different states convicted of armed crimes.
40% of the felons surveyed reported stealing firearms. 12% of the felons stole guns for personal use. So a lot of gun thefts are sold to other criminals. Sources stolen from included:
37% from stores,
15% from police,
16% from truck shipments,
8% from manufacturers,
21% from individuals.
So in a hypotherical world with no civilian guns, the military and police would have firearms, there would still be "cop shop" gun stores, manufacturers, requiring shipments, all the current sources of stolen guns, except private individuals.
FBI reports 430,000 gun crimes per year. Ignore ATF NIBIN crime scene ballistics stats that one gun may show up in multiple crimes in the the course of a year. Assume for the sake of argument each crime represents one gun, one criminal. How many of those 430,000 guns would need replacement in a year? How many would be ditched, broken, seized by police, etc? How many guns stolen solely from police and military would it take to maintain the current gun crime rate?
Look at Australia, in the face of the 1996 "buy back" of 640,0o0 semi-auto and pump-action long guns. Current news reports in reputable Aussie newspapers easily findable on the Internet detail busts of pistol smuggling rings allied with drug smuggling rings, and basement and garage machinegun factories run by "bikies" (what we call Outlaw M.C.s). That is the future of a gun free utopia. Sports guns, hunting guns, collectibles, self-defense guns taken from the law abiding and destroyed, and the bad guys better armed than before.
Maybe the Loughners of the world may or may not be able to tap into the black market sources used by the NIJ armed and dangerous felon sample, or the drug or "bikie" gangs of OZ, but there are a lot more reports from Australia of street shootings over what we would call "dissing" by people who are not drug gangsters or motorcylcle clubs, meaning the black market spills over throughout society, especially ampong the lawless and desperate.