Tatoz:
What do you mean by no sulfur Mg and Fe? Do you mean Sulfur, Manganese and Selenium?
We machine low sulfur, low inclusion VIM/VAR stainless steel every day. The Sulfur in 316 is specified at a maximum of 0.030%, and the producers add Sulfur back in for product intended for fabrication by machining, as Sulfur significantly improves machinability. The sulfur exists in the stainless as precipitates with Manganese, and these precipitates have a lubrication and chip-breaking effect during machining. But the precipitates also are sites for initiation of corrosion on end grains and have negative effects.
When you specify a low sulfur stainless, Sulfur in the range about 0.001%, you will find that you need to reduce the machining speeds approximately 30%. Do not reduce your feed rate too much, however, as the stainless will develop a work-hardened surface which is very difficult to machine. Use a good quality machining fluid, and plenty of it. Preferably carbide tooling, but if you use tool steel, use a grade with good hot hardness characteristics. The chips will tend to be stringy and will require periodic removal to avoid damaging the part.
Be aware that Sulfur also has a tremendous effect on welding, also. As you reduce the sulfur to very low levels, the depth to width ratio of your weld decreases markedly and more heat input is required.
If I can help further, let me know.