How is King Bradley's sword so sharp? Throughout all of Fullmetal Alchemist Manga, King Bradley chopped his way through everything, from stone to arms to automail.

How did it get to be so sharp? What did the King use to sharpen his sword?

An aside: the sharpness of his sword seemed to transfer to any bladed weapon he used. Was it a side effect of his homunculus-ness?
They're so sharp because he takes care of them. The true power behind his swords are his swordsmanship, superhuman strength and incredible speed. Everything King Bradley uses to fight with is really just ordinary weapons. There is a scene in the brotherhood series (I'm aware you mentioned the manga but your overall question is generic) where he even picks up two dagger and starts to fight the old man with no problem.

With the right amount of precision and strength it is possible to slice through some really dense materials (Including metals) with a really well made sharp sword. Keep in mind that it is still just an Anime/Manga.