Density depends on both the mass and the volume of an object. If you cut a bar of gold in half, you would have two bars with half the mass of the original bar. However, each bar would also have half the volume of the original bar. The density of gold does not change.
To make clay float in water you have to shape it into something wide enough and roughly bowl-shaped so that it can displace enough water to compensate for its mass, just like a real boat.
