I cut inlay, both long grain and cross grain, into 1mm wide strips from 2mm thick sheets. It's tricky but not impossible.
The big problem is that, once you get down to dimensions like these, there's actually no such thing as a zero clearance saw plate with normal saw blades, because the teeth are wider than the saw plate. Consequently the air turbulence around the blade is enough to lift and shatter the workpiece. I get around this by using special blades where the teeth and the plate are the same width (but that gives you problems with the riving knife) or I go to extraordinary lengths to support the workpiece through the cut.
If you're cutting to these dimensions from commercial veneer, which is usually 0.5-0.6mm thick, then you're far better using a knife or a traditional hand held veneer saw.