This sounds very much like _The World on a Turtle's Back_ , an Iroquois creation story. Originally passed down orally, a version was written down by the Iroquois author David Cusick in _Sketches of the Ancient History of the Six Nations_ in 1827.
The story concerns two twins, one right-handed and the other left-handed who live on the back of a turtle. They quarrel and fight, and the right-handed twin eventually throws his brother off the turtle into the void. When he went home his grandmother called him a murderer, and in anger he killed her too. As the question states, the story is often compared with the "Cain and Abel" story of the Bible, although there are also considerable differences between the narratives. Many variants of the story exist. One of the more common types is available here, although comparing with Cusick's version reveals the large degree of variation between them.