Mineralized materials are gaining increased interest recently in a number of fields, especially in bone tissue engineering as bone replacement materials as well as in the architecture-built environment as structural building materials. Until the moment, there has not been a unified sustainable approach that addresses this multi-scale application objective by developing a self-mineralized material with minimum consumption of materials and processes. Thus, in the current study, a hydrogel developed from sodium alginate, gelatine, and calcium phosphate dibasic (CPDB) was optimized in terms of rheological properties and mineralization capacity through the formation of hydroxyapatite crystals. The hydrogel composition process adopted a three-stage, thermally induced chemical cross-linking to achieve a stable and enhanced hydrogel. The 6% CPDB-modified SA–gelatine hydrogel achieved the best rheological properties in terms of elasticity and hardness. Different concentrations of epigallocatechin gallate were tested as well as a rheological enhancer to optimize the hydrogel and to boost its anti-microbial properties. However, the results from the addition of EPGCG were not considered significant; thus, the 6% CPDB-modified SA–gelatine hydrogel was further tested for mineralization by incubation in various media, without and with cells, for 7 and 14 days, respectively, using scanning electron microscopy. The results revealed significantly enhanced mineralization of the hydrogel by forming hydroxyapatite platelets of the air-incubated hydrogel (without cells) in non-sterile conditions, exhibiting antimicrobial properties as well. Similarly, the air-incubated bioink with osteosarcoma SaOs-2 cells exhibited dense mineralized topology with hydroxyapatite crystals in the form of faceted spheres. Finally, the FBS-incubated hydrogel and FBS-incubated bioink, incubated for 7 and 14 days, respectively, exhibited less densely mineralized topology and less distribution of the hydroxyapatite crystals. The degradation rate of the hydrogel and bioink incubated in FBS after 14 days was determined by the increase in dimensions of the 3D-printed samples, which was between 5 to 20%, with increase in the bioink samples dimensions in comparison to their dimensions post cross-linking. Meanwhile, after 14 days, the hydrogel and bioink samples incubated in air exhibited shrinkage: a 2% decrease in the dimensions of the 3D-printed samples in comparison to their dimensions post cross-linking. The results prove the capacity of the developed hydrogel in achieving mineralized material with anti-microbial properties and a slow-to-moderate degradation rate for application in bone tissue engineering as well as in the built environment as a structural material using a sustainable approach.