Suggest a procedure to separate iron filings form sawdust. Explain why the procedure works?

We could use a magnet.

Iron is made up of a lot of litle magnetic sensitive molecules that tends to react to the presence of a magnetic field. A piece of iron will "feel" the magnetic field and orientate itself according to it. [iron fillings around a magnet]

Sawdust is an organic molecule that like a bundle of cooked spaghetti doesn't react a lot to the magnetic field or at least not so dramatically.