Diana originally acquired the God Killer from a special tower on Themyscira, which contained the "many gifts" that the Gods gave the Amazons, believing it would be the only thing that would slay Ares the God of War.
Diana notably used it to kill General Ludendorff, stabbing him through the heart with it, as she wrongly believed him to be Ares. During their battle, Ludendorff briefly disarmed her and tried to use the sword against her, until she disarmed him and took it back.
The sword was ultimately and casually destroyed by the real Ares, who revealed that the so called God Killer sword was not the true "God Killer" meant to kill him, but that Diana herself was. The blade was almost completely disintegrated, but the rest of the sword remained intact. What became of the its remains is unknown.
At some point, she replaces the God Killer with the Sword of Athena, using it as one of her weapons.
The God Killer is an incredibly sharp and durable weapon, showing no apparent damage after Diana's extensive use of it during World War I. It was likely also magical in nature, as are many Themysciran weapons. However, it can still be destroyed by the divine power of an Olympian God, as Ares eventually did.