The staff at Kojima Productions had the "cut anything" concept realized, according to Andriasang's report of the latest Hideraji podcast. They also had the motion capture done and a story written ... but the rest was in the air. Without a clearer direction, Kojima decided to end development.
Platinum Games studio reps happened to visit, the story goes, and expressed their excitement for the project, leading to their assignment to complete the game. It was Platinum's idea to change the story, and they also offered the concept of "a game where it feels so good to chop things up that you would die," as Andriasang translates it. We think that's a more promising concept than a game where it feels good to chop things up, and then the game dies.