The Bible required that animals killed for food had to be bled , and the blood not eaten.
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The Law did allow an Israelite to eat the unbled meat of an animal they found already dead (this means all the blood was still in the meat). And it allowed Israelites to sell unbled meat to Gentiles.
It goes back to the simple rule that when a life is taken the blood is poured out in acknowledgement of that life. In a blood transfusion, no donor has given their life, therefore, there's nothing to "give back" by pouring out the blood.