[burn13090]

How would one go about separating a mixture of amalgam filling (silver and mercury) and 14 Karat Gold (gold and copper)?

You must retain all materials, and they must all be metals.

Is it possible that it is as simple as heating them until each element melts in succession?

Ag Melting Point:  1234.93K
Hg MP:  234.32K
Au MP:  1337.77K
Cu MP:  1357.77K

[agrobert]

What are your thoughts?
Alloys and amalgams often have melting ranges that are different from their respective constituents.  In melting an amalgam liquid and solid phases generally coexist.  The physical properties of amalgams and alloys are changed.  I think you need more research on your part.