How to cut stainless steel sheet without burning it?
As you have implied, heating the metal is actually changing it near the cut and causing it to discolor.  There's not soot or anything you can clean off - the metal is changed.  You may be able to sand off the surface of the metal near the cuts to remove the discolored metal on the surface, but this will lead to a cut that doesn't look very clean and some discoloration may remain.

The other choice is to cut the metal without heat.  Angle grinders don't really cut - they sand their way through the metal creating a massive amount of heat.  One tool that actually cuts through the metal is known as a "nibbler".  They come in many forms.  Hand operated, air powered, electric, and as a small attachment for an electric drill.

They are basically a small punch that nibbles of small bits of metal.  They do this very quickly so the result looks like a straigt cut.  The issue is that many of the tools that I found top at at 16ga (1.5875mm) or 14ga (1.984375mm) sheet metal.  Your 1.5mm sheet is going to be at the top end of their capabilities, but if you choose a quality tool and don't try to move too fast, I think you'll be ok.