From your description and my own viewing of the video, one might conclude that Nick was dead, or drugged, before they sawed his head off.
There was a quantity of blood, but it was not pumping out vigorously as one would expect if the heart were still beating, so it is likely, hopefully, that he had died before the grisly beheading.
I saw the blood, too. But it, as you point out, appears to be running out of a corpse and not a living body.
Then who the hell screamed?