The daily sacrifices are usually killed with a fast acting, fairly painless poison (to prevent the waste of any blood) and are then blood let on the appropriate altar.
I just did some research, and it appears that if the person recently died, they would not bleed as much, because there's no working heart to pump the blood. After several hours, the blood dries, thus making them unable to bleed at all.
Just a suggestion, but maybe you could replace it with some drug that knocks you out, or gets you high enough to not feel pain.
Sacrifice, by its nature, is the exchange of future potential for current gain. Otherwise, it's simply butchery. So does your setting have magic? Idiot psychology? Or hungry cannibals? That determines pretty much all other factors.What kind of people are sacrificed? Slaves, criminals, prisoners of war, what other kinds of people? How do they sacrifice them, and how painful or brutal are their deaths?