interesting one! i looked it up, and there's actually a question from readers on it.

Here's the gist:

God’s law on blood is very clear. Blood is not to be used as food and, when withdrawn from a body, it is to be poured out on the ground. (Gen. 9:3, 4; Lev. 3:17; Deut. 12:16, 23, 24; Acts 15:20, 28, 29) Christians certainly would not wish to do anything in violation of Jehovah’s law on blood. Love for God and for the righteous laws and principles of his Word calls forth that response from them in matters pertaining to blood.

Since God’s law on blood has not been altered over the centuries, Christians today realize that they are bound by it. Please note, however, that it is not fear of some reprisal that moves them to comply with Jehovah’s law on blood. They do not obey God’s law simply because violation of it might result in the imposing of sanctions by the Christian congregation of which they are a part. They love what is right. Furthermore, because of their love of God’s law they will not rationalize or seek ways in which it appears possible to circumscribe it with seeming impunity.

How, then, must we answer the question, Would it be a violation of the Scriptures for a Christian to permit a veterinarian to give blood transfusions to a pet? By all means, to do so would be a violation of the Scriptures. To use blood for transfusion purposes, even in the case of an animal, would be improper. The Bible is very clear in showing that blood should not be eaten. It should not be infused, therefore, to build up the body’s vital forces, either in the case of a human or in the case of a pet or any other animal under the jurisdiction of a Christian.

It then continues talking about animal food with blood in it. Basically the same principal applies: it's the _blood_ that is sacred to Jehovah. we wouldn't want to misuse it.