The moon's effect on the body has nothing to do with the fact that humans are made of mostly water. The moon does exibit tidal forces on a human body, but they are so minute, that nothing physically observable arises from it. If the moon just vanished, it would affect the way the Earth rotates, how it orbits, and the Earth's weather works in the first place, but no direct effect on the human body. Now there may be phychological effect due to the absence of the moon, but if the moon left Earth's orbit very gradually, like it will eventually, there will be no phychological effect either. So the moon leaving will have no direct effect on a human, but many indirect effects like longer days, stranger weather, messed up currents will effect humans for obvious reasons.

However, if you are a Saiyan or a warewolf, the effects are enormous, but thats an entirely different story.