This would probably work for about 1 month. After everyone finished reeling in horror from the senseless murders of many of their families and loved ones, some subset of the people would quickly realize that all the competition had just been eliminated from the drug market, rendering it extremely profitable and lucrative. Time to stop whatever they were doing to start producing and selling drugs instead.
At which point, we kill them as well. And yes, I really am being serious.
For countries which have implemented this proposal or slightly watered down versions: see Singapore and China and note that even though they are in the middle of a drug heavy region, they have still managed to keep their countries relatively drug free.
I guess I just don't see the end goal of what you're proposing. What is the merit of having a drug-free society if it comes at the cost of damaging or destroying productive, happy human lives? Do you think the world you are describing would be a better world to live in than the one we have today? Or one in which more drugs were legal?
As various other commenters have pointed out, between prescriptions, over-the-counter pills, vitamins, and additives in the foods we buy, we're all drug users. This whole argument seems to rest upon an absolutist view that all currently illegal drugs are absolutely destructive and have no merit.
Countries like Singapore and China have radically different ideological approaches to policy than most Western nations. They are comfortable enforcing absolutist positions that limit individual freedoms. Such a position is against America's founding principles. They may statistically report less drug use, but is their society actually any better off for it?
From what I have seen from night clubs in Shanghai, there is a lot of extasy going around. And my friends in China have no problem getting hold of cannabis...
Now they are taking big risks and I wouldn't take those kind of risk if I were them but it convinced me that however strict the laws are against drug it doesn't stop people from taking them...
(Were you really being serious?)