Is there a less literal translation? What would this actually mean?
This Japanese sentence sounds quite unnatural to my native ears. I looked it up in the original source (Tatoeba), and it turned out that the author of the Japanese and the English sentences is a Brazilian Portuguese native speaker… It may mean something special in a Brazilian proverb, but both the Japanese and the English sentences don’t make sense…
The only interpretation I can deduct from it is “I decided not to undergo any surgery. So, I don’t need a heart for organ transplant. Please opt me out of the waiting list” – i.e. a “heart” means a physical organ, not emotional one. If the author meant so, I would propose:
Even if the original sentence with 心 (こころ) is replaced with 心臓 (しんぞう), 私はもう心は必要ありません is still grammatically awkward because of the reduplication of は twice. It should be inserted に after 私.
XにYは必要ありません is “Y is not needed for X”. Therefore, X is not a subject (doer). に is a particle to mean “for/to/toward” (beneficiary of something). You can say both 私「に」必要ありません and 私「には」必要ありません. The latter (with は) implies that “other ordinary people need a heart, but I don’t”. Particle は is often used to highlight and compare two different (invisible) situations.