Can I print jewelry without any loss of the precious metal? What is the 3D printing technology that allow to have minimal loss in precious metals when 3D printing jewels?
The jewelry industry typically uses printers that print in wax, and transform the models into precious metal by lost wax casting. Statasys offers wax printing in their Solidscape line, 3D systems offers ProJet. With this process there is basically no waste, since you can remelt the casting sprues.

I am not aware of printers that print directly in precious metal. It might technically be possible with DMLS but you have to fill up the entire machine with metal powder, which is cost prohibitive (and potentially more wasteful).