In aspects, embodiments of the present invention provide devices, systems and methods for managing cuttings formed during drilling of a subsea wellbore. By managing, it is meant the processing, storage, transportation and disposal of the cuttings. In an exemplary application, an offshore rig adapted to drill the wellbore uses one or more a selectively buoyant containers to transport the cuttings. The containers are positioned adjacent the offshore rig. In one arrangement, the containers are submerged to a selected depth below the water's surface. A transfer unit flows the cuttings from the offshore rig to the container via a conduit connected to the container.