With a handsaw, one trick is to score through the veneer with a straightedge and sharp knife. Then use a finely-toothed blade, and let the blade do the work rather than trying to force it into the wood --always good practice, but especially in this situation. You may want to experiment with cutting angles, to cut less perpendicularly to the veneer surface.
With power tools, using a sharp, finely-toothed blade and a zero-clearance guide or faceplate can make a huge difference.