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In the fight scene near the Sanctum Santorum in Avengers: Infinity War Cull Obsidian's hand got cut off by a closing portal, but in the battle of Wakanda it was grown back to normal.
Does he have Regeneration power?
No, he doesn't have regeneration power.
He got an artificial arm like Bucky and Luke Skywalker.
Since Thanos has been replacing Nebula's body parts with machines, we know he is quite capable at doing cybernetic enhancements.