That's correct. By melting or smashing it, you would just be breaking it up. The liquid or fragments you'd be left with are still gold. You could only "destroy" the gold by altering its atomic structure. Same with any element.
Sodium cyanide solution will also dissolve gold. This is the process used commercially to recover that gold that cannot be recovered by mechanical means alone.
Incidentally, a sort of 'opposite' to this is using hydrofluoric acid (HF). This highly reactive acid is capable of dissolving silicate minerals but it will not dissolve gold.. It is sometimes used to dissolve the rock matrix from around gold nuggets, leaving intricate lattice structures behind. (though this is not used on a commercial scale) Oh, and as glass is a silicate, you can't keep hydrofluoric acid in glass bottles!!
Feederzombie is right, though he should have written nuclear structure rather than atomic structure. Scientists have, I believe, made other nuclei into gold nuclei by bombarding the other nuclei with high energy sub-atomic particles such as alpha particles. There seems to be no good reason why bombarding gold nuclei with sub-atomic particles should not result in the "destruction" of the gold nuclei and the creation of something else. Remember, matter cannot be created or destroyed (except relativistically).
Yeah, nuclear structure not atomic structure. Specifically, you'd have to alter the number of protons in the gold nuclei, as it's that which determines the element. Altering the number of electrons would make gold ions, and changing the number of neutrons would result in gold isotopes. Not the same as gold atoms, but still technically gold.