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So it is your attack turn, you declare a sole attacker bloodthrone vampire, your opponent does not declare blockers, then you proceed to beat the **** out of him by sacrificing your dudes.

A super legit play.

Keep up the good magic.

There are multiple steps to combat.

Start of Combat
Declare Attackers
Declare Blockers
Damage
After Damage/End of Combat
(Also if any creatures have first strike it creates an additional damage/after damage step)

You gain priority during every step, except where the damage is actually dealt (but you have priority before and after so that's not really relevant). The play you've mentioned would take place after he declares that he is not blocking, before the damage step. He can't "take the damage" without you gaining priority to sac your creatures to make him stronger after he chooses not to block.

If you waited til after the damage step, you could still sac the creatures but additional damage would not be dealt. That might be relevant for something like Fling or Mutilate but in general you'd still want to do that before the damage step for additional damage there.