There is a reply from Dr Alaa’ alSalim (http://vb.almahdyoon.org/showthread.php?t=16273), it is about donating blood and donating body parts :
In the name of Allah the Most Merciful, the Intensely Merciful, and all praise is due to Allah, and may Allah send peace and prayers upon Muhammad and his family, the Imams and Mahdis.
These are some of the answers from Sayed Ahmed alHasan (as) in relation to donating body parts, I will copy them from the book "Ajwibat alFiqh - Mutafariqah" :
Question 113/ Is it permissible to donate the organs of the dead person after his death?
Answer: It is permissible for a person to determine by a Will that he donates one of his organs or even more than one of his organs after his death and he will be rewarded for this Inshallah if he donated it to a believer or to someone who delivers it to believers, and Allah is the grantor of success.
Question 114/ Is it permissible for the guardian of a dead person to donate or sell one of his organs [dead person] to someone alive to utilize it?
Answer: Selling is impermissible, and it is permissible to donate if the believing guardian is the father, mother, son or daughter.
Question 115/ Is it permissible to donate or sell an organ of an alive person to another one alive as well?
Answer: Selling is impermissible, and donating is permissible.
From this it is seen that donation of organs is to a believer, not to others, and in respect to the conditions mentioned in the answers above.
Concerning the donation of blood, it is permissible if it was from a non-muslim to muslim. This is a question and the answer from him (pbuh) in this concern
Question: What is the ruling of blood donated from a disbeliever or Nasibi to a muslim?
Answer: No problem with that.
As for the blood donation of a believer to others, I don't know about it and we shall wait for the answer of the Imam (pbuh) concerning it.
May Allah grant you success to all that is good
19/ Shaaban/ 1433
There is also an answer which encourages blood donation instead of cupping:
Answers of Jurisprudence (Ajwibat alFiqh) volume 3 question 97:
Question: What is the ruling for Hijama (cupping) with regards to the woman, because I heard from one of the brothers the he read a narration which says that Hijama is Makruh (not recommended) for women specifically?
Answer: You can have the benefit of Hijama by donating blood whether it is for the man or woman, may Allah give you success and guide your steps.