In this paper, we present design principles for cutaway visualizations that emphasize shape and depth communication of the focus features and their relation to the context. First, to eliminate cutaway-flatness we argue that the cutaway axis should have an angular offset from the view direction. Second, we recommend creating a box-shaped cutaway. Such a simple cutaway shape allows for easier context extrapolation in the cutaway volume. Third, to improve the relationship between the focus features and the context, we propose to selectively align the cutaway shape to familiar structures in the context. Fourth, we emphasize that the illumination model should effectively communicate the shape and spatial ordering inside the cutaway, through shadowing as well as contouring and other stylized shading models. Finally, we recommend relaxing the view-dependency constraint of the cutaway to improve the depth perception through the motion parallax. We have identified these design principles while developing interactive cutaway visualizations of 3D geological models, inspired by geological illustrations and discussions with the domain illustrators and experts.