To research the religious aspect of bloodless surgery, as far as concerns Jehovah's Witnesses, the Society has a website:
Jehovah’s Witnesses: Watchtower Society Official Web Site This is the only official website of the Society, so you'll be assured of finding the correct information.
This link will take you to specific information:
Publications Available - Jehovah’s Witnesses Official Web Site
On this page, scroll down until you reach the subtitle 'Brochures', the second listing under that will be the booklet entitled, 'How Can Blood Save Your Life?' This provides a more indepth explanation of why Jehovah's Witnesses refuse blood based upon a deeply held religious conviction.