Strip samples of widths ranging between 5 mm and 30 mm were cut from different types of non-oriented magnetic steel sheets by means of guillotine shear cutting and water-jet technology and characterized from DC to 400 Hz. The measured magnetization curves and energy losses and their dependence on the strip width, that is, on the proportion of damaged to pristine sample cross-section, have been analyzed and modeled. While confirming an expected lighter material deterioration engendered by water-jet cutting, the analysis of the results remarkably shows that the evolution of the normal magnetization curve and the quasi-static magnetic losses with the width of the cut strip follows a hyperbolic law. This novel finding permits one to predict, using minimum pre-emptive information, the evolution of normal magnetization curve and hysteresis loss from indefinitely wide to narrow fully degraded strip. The highly strain-hardened region is, in this way, estimated to propagate from the strip edge by about 2.1 mm and 1.6 mm in the punched and water-jet cut samples, respectively. The dynamic loss behavior is assessed by analysis of the excess loss component, in accordance with the statistical theory of losses. A small to moderate increase of the dynamic loss (i.e. of the excess loss) with decreasing strip width is found, following to some extent the behavior of the quasi-static loss.