From Nov. 2006 Kingdom Ministry p. 3
Title: How Do I View Blood Fractions and Medical Procedures Involving My Own Blood?”
“How Do I View Blood Fractions and Medical Procedures Involving My Own Blood?
The Bible commands Christians to “abstain from . . . blood.” (Acts 15:20) Thus, Jehovah’s Witnesses do not accept transfusions of whole blood or the four primary components of blood—namely, red blood cells, white blood cells, platelets, and plasma. They also do not donate or store their own blood for transfusion.—Lev. 17:13, 14; Acts 15:28, 29.”
According to this, if the act of receiving blood fractions from donated and stored blood violates the Bible’s command to “pour its blood out”, then it wouldn’t matter whose blood it is, whether that of yourself or anybody else. The Bible doesn’t say you can eat the blood of someone else's animal, but not of your own. Leviticus said, “you must not eat the blood of ANY sort of flesh…”
Not that the blood policy makes sense anyway, but it's possible to use the JW/Watchtower's rules against themselves.
(Leviticus 17:13, 14) 13 “‘If one of the Israelites or some foreigner who is residing in your midst is hunting and catches a wild animal or a bird that may be eaten, he must pour its blood out and cover it with dust. 14 For the life of every sort of flesh is its blood, because the life is in it. Consequently, I said to the Israelites: “You must not eat the blood of any sort of flesh because the life of every sort of flesh is its blood. Anyone eating it will be cut off.