We investigated the effect of partial dehydration under mechanical stress in the properties of alginate hydrogels. For this aim, we characterized the mechanical properties of the hydrogels under tensile and shear stress, as well as their swelling behavior, macroscopic appearance, and microscopic structure. We found that the processes of dehydration under a mechanical stress were irreversible with fully rehydration being impossible. What is more, these processes gave rise to an enhancement of the mechanical robustness of the hydrogels beyond the effect due to the increase in polymer concentration caused by dehydration. Finally, we analyzed the applicability of these results to alginate-based magnetic hydrogel grippers that bended in response to an applied magnetic field. Remarkably, our study demonstrated that the dehydration of the magnetic hydrogels under compression facilitated their bending response.