I need to know what is the mental illness where people desire fully functioning parts of their bodies to be amputated?

Munchausen Syndrome: Munchausen syndrome is a condition in which the individual wants to have unnecessary procedures performed - often times over and over again. Even worse is the condition munchausen by proxy - a parent wants these procedures performed on their child. Hope this helps.

Psychosis too: I agree with my colleague about munchausen's as one possibility. But i've also known people who were very psychotic (such as schizophrenic or schizoaffective) who self-amputated functional body parts. Wanting to remove body parts is not enough to make a diagnosis, so psychiatric consultation is wise in such cases.