The basic ruling is that treatment must be with lawful things, which are permitted by the authority of Shari`ah. However,
if there is no way to strengthen or treat the patient except through blood transfusion as a prescribed means of rescue from the disease or weakness, provided that specialist doctors think the patient will most probably benefit from it, there will be nothing wrong with treating them with it and alleviating their illness and weakness through transfusion of blood donated by others. Allah (Exalted be He) says:
He has forbidden you only the Maitah (dead animals), and blood, and the flesh of swine, and that which is slaughtered as a sacrifice for others than Allâh (or has been slaughtered for idols, on which Allâh’s Name has not been mentioned while slaughtering). But if one is forced by necessity without wilful disobedience nor transgressing due limits, then there is no sin on him. Truly, Allâh is Oft-Forgiving, Most Merciful.
He (Exalted be He) also says:
...while He has explained to you in detail what is forbidden to you, except under compulsion of necessity
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family and Companions.