I'm not aware of "Executioner Round" as an official Magic: The Gathering keyword or ability. It doesn't correspond to any mechanic I can verify, so I don't want to invent rules for it and risk misleading you.
It's possible you're thinking of a similarly named card, a mechanic from another game, or a misremembered term. Some things it might be confused with: "Executioner's Capsule" (a card that destroys a creature), or keyword actions like "exile" or "destroy."
If you can share the exact card name or where you saw "Executioner Round," I can give you an accurate rundown of how it works and its Commander relevance. I'd rather get you correct info than guess at a mechanic I can't confirm exists.