In a cutting tool rotatable about a tool axis, a reversible cutting insert is removably secured in a tool body. The cutting insert has opposing top and bottom end surfaces interconnected by a peripheral surface, and a median plane located therebetween. The peripheral surface includes four side surfaces alternating with four corner surfaces, the side and corner surfaces intersecting the top surface to form top major cutting edges and top corner cutting edges, respectively. Each side surface has a median surface and a top major relief surface. Each top major relief surface forms an acute internal top major relief angle with the median plane, and the median plane intersects the four median surfaces to define an imaginary median square. In a top end view of the cutting insert, the four top major cutting edges define an imaginary top major square rotationally offset from the imaginary median square.