This is part of Scripture’s consistent message that the word “blood” means “death”. (In a medical procedure, “blood” never symbolises the death of its previous owner. And the donor’s flesh is not eaten.)
But then there was a change in scripture. The Law upon which all this was based would no longer be valid and any prohibition against blood made in times past was now changed by our Lord to include it since it would now be an essential ingredient, even a mandatory one for our salvation. John 6:53 Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you. Any blood prohibition made in times past would now be allowed. Such a statement could not be made for any reason unless such prohibitions were brought to an end. The cup we drink means his blood, not just some supposed symbolic reference to it. We would not think of it as wine anymore but as blood when it was consumed. The use of wine was simply a way to do this since the man giving this command would not have enough blood for the whole world to eventually drink anyway.
Mt 26:28 For this is my blood of the new testament, which is shed for many for the remission of sins.
Eph 1:7 In whom we have redemption through his blood, the forgiveness of sins, according to the riches of his grace;
Col 1:14 In whom we have redemption through his blood, even the forgiveness of sins:
The use of blood to save life was now allowed and scriptural. This one reason does not exclude it for being used for medical purposes as well since permission to use it was granted to mankind. And it is nothing more than an organ transplant when given anyway. But then a problem developed that would not be solved for a long time. James wrote a letter that he gave to Paul for distribution and h is stipulation looked quite innocent on the surface. It contained deeply ingrained matters of contention of little concern to Gentiles. You will notice however that it was directly associated with Moses and the Law, dealt with blood and was intended ONLY for Gentiles. One doctrine for Gentiles and another doctrine for Jews was the result. It contradicted out Lord's teaching regarding the use of blood and directly impacted on their salvation. Some have attempted to apply this requirement to the pre-law writings of Moses as if this makes some kind of difference but that no longer matteres. And we know from Scripture that James was concerned with the Law itself and continued to observe and teach it in Jerusalem. He tried to force Paul to submit to it as well (Acts 21:24). So by mixing in some good with the bad many have taken this letter as doctrinal when in reality it was an error brought out in scripture that would take 40 or more years to correct by Paul and some have still not corrected it.