Stress relaxation is an important design parameter of biomaterials that can provide an artificial microenvironment mimicking natural extracellular matrix (ECM). Here, we report a novel hydrogel platform based on sodium alginate (NaAlg) with tunable stress relaxation. We first developed a new synthesis route to introduce alkoxyamine functional groups into the alginate polymer backbone. By mixing the resulting polymer (NaAlg-AA) with aldehyde containing oxidized alginate (NaAlg-Ald), oxime cross-linked alginate hydrogels were prepared. We demonstrate that highly tunable stress relaxation and mechanical properties can be achieved by systematically varying the composition (concentration, polymer mixing ratios, degree of oxidation of NaAlg-Ald) or environmental factors (pH, temperature, and use of catalyst). Combined with the natural capability of the alginate to be cross-linked by divalent cations, the developed hydrogel formations possess the unique capability of dual cross-linking mechanisms with different gelation kinetics. We demonstrated that this dual cross-linking capability can (i) be utilized for the creation of hydrogels in microbead or microthread geometries and (ii) be useful for biomedical applications that require both the fast encapsulation of cells in hydrogels (fast calcium cross-linking) and the provision of controlled viscoelastic environments to cultured cells for an extended period (durable oxime cross-linking). With biocompatibility confirmed by the culture of a B-cell line encapsulated within the developed hydrogel, this novel hydrogel platform provides a good prospect in various applications where stress relaxation plays a key role in cell matrix interactions.