Could you separate the sodium from the chlorine by crushing the salt crystals

No, you cannot.

The distinction is made in the fact that the sodium and chlorine atoms are bonded chemically, while the crushing of the salt is a physical change. A physical change is one that does not have the ability to change the identity of the substance. Such changes include crushing, boiling, melting. In order to separate the chlorine and sodium atoms, you must make them undergo a chemical change, for example add the salt to sulfuric acid and make it react.