Continuous circulation and rotation drilling system, comprising: a top drive; a mud circulation system; a drill assembly including a drill pipe; a clamp device. The continuous circulation and rotation drilling system is drivable between a first condition and a second condition. In the first condition, the drill assembly and the clamp device are mutually disconnected. In the second condition: the main body of the clamp device is in a closed configuration and the drill assembly is partly enclosed in an inner housing of the clamp device; the mud circulation system feeds drilling mud through a radial opening of a main body of the clamp device; one or more actuating groups of the clamp device are activated to rotate the drill pipe around its longitudinal axis.