The scriptures have not mentioned organ donation since it was not a practice during ancient times. This is a recent phenomenon. As it was unknown during ancient times, it cannot be said that the scriptures support this. Our elders hesitate in doing something that is not supported by the scriptures and only practice what is ordained by the scriptures. The wise and noble will be reluctant to accept that which is not mentioned by the scriptures. Similarly, we should be hesitant because we must consider what rights we have to donate organs of a physical body granted by Bhagavan, to another person.
Consigning the physical body to fire at the end of life is counted as a performance of a homam, which is accompanied by mantras; fire is lit to the funeral pyre accompanied by chanting of mantras. Hence, the scriptures say the physical body should not be missing any parts and offered as a whole object.