Reddit: So You Thought You Destroyed the Sword of Crota?
While it's true that you turn in "Blade Shards" at the end of the mission, the in-game description goes like this:
"Fragments of a Swarm Prince's broken blade. Return these to your Vanguard mentor as proof of your success against this ancient enemy."
I don't know about you, but the shards of a Swarm Prince's blade seem rather different from the shards of the Sword of Crota itself. One would think that might be mentioned in the description of the item if it were the real deal.
Besides that, there's never any action of destroying it. Nothing about a sword vanishing into thin air denotes the breaking down of said sword into shards. And one would think the destruction of a sword like that would be worth some kind of cut scene (just think back to the shard of the Traveler we free up), especially if the sword contains the Light of the countless Guardians it's killed.
So what happens? Where dose the Sword of Crota go?
EDIT: In the Grimoire for the Sword of Crota, it reads:
"The Swarm Princes are dead, and the Sword of Crota is gone. Though many still believe Crota's return is inevitable, that thousands of weapons will be forged in His name, I have faith that we are now one step closer to ending the Hive's reign over the Moon." - Master Rahool
His word choice implies the Sword just vanished, and was not, in fact, transmatted anywhere. Especially consider the fact that your Ghost says something like "The Cryptarchs are never going to believe this," which implies they're just being told about it rather than offered any tangible evidence.