JOEL - The Church position is not against the practice of body part donation. Here is a policy statement from the Church about this subject:

Because the transplanting of body parts raises some concerns regarding ethics and moral issues, the Church has issued the following statement: "Whether an individual chooses to will his own bodily organs or authorizes the transplant of organs from a deceased family member is a decision for the individual or the deceased member's family. The decision to receive a donated organ should be made with competent medical counsel and confirmation through prayer" (General Handbook of Instructions, 11-6).

Actually, if you think about it, blood could be considered a part of the body as well. If our General Authorities were opposed to blood transfusions, many of them would not be alive today.