If a person or animal has their head severed or cut completely off then the person may die instantly but their head may be conscious for around 2 minutes to 10 minutes.
I remember reading somewhere a lady who had her head cut off in an accident I believe was still conscious and her eyes were moving for at least 10 minutes before the head lost consciousness.
That would be freaky to go to an accident like that and have to pick up someone's body parts and see there head still conscious.
Most heads that are severed are rendered unconscious within a few minutes to instantly.
But of course when someone gets into a bad car accident and the persons head is cut off completely they may have had consciousness in their head for a few minutes or longer before emergency personal got to the scene.
But when emergency crews arrive at the scene of a major accident and someone has their head cut off or other body parts dismembered then they are usually dead upon arrival on the scene.