It has been done before but is highly controversial. If you detusk, they will probably die faster. Male Elephants use their tusks to fight or to defend themselves from attacker. All elephants use their tusks for foraging, removing bark from trees, searching for water, digging riverbeds for water etc.

Elephants that do not have tusks have adopted other ways of surviving by the time they reach adulthood. However if you detusk a grown elephant, there is a good chance it will not survive.

Let me play the devil's advocate in this story - What is the worst thing that will happen if Elephants cease to exist? We once had the Dodo, the giant moa, the Haast's eagle e.t.c. in the last 100 years we have had the marspial tiger, the Pinta tortoise, the monk seal, the caspian tiger among other species disappear... why do we think the elephant's demise will affect us in a way dissimilar to the disappearance of the dodo? It would have been nice to see a dodo but it's all sentimental! extinction of species is a way of 'life'....

Nature is already working its way out!!!

My take: There have been dozens of Proboscidean species that have gone extinct. Some are depicted below. The most recent ones have gone extinct due to being hunted by mankind. We should avoid repeating the same mistake. Mankind has already caused a lot of species to go extinct. If we can prevent this from happening, we should. Our lives would be more enriched if we still has mammoths, and mastodons roaming around not to mention the more ancient ones like stegodons, gomphotheres