Alginate hydrogels have applications in biomedicine, ranging from delivery of cells and growth factors to wound management aids. However, they are mechanically soft and have shown little potential for the use in bone tissue engineering. Here, the viscoelastic properties of alginate hydrogel beads mineralized with calcium phosphate, both by a counter-diffusion (CD) and an enzymatic approach, are characterized by a micro-manipulation technique and mathematical modeling. Fabricated hydrogel materials have low mineral content (below 3 % of the total hydrogel mass, which corresponds to mineral content of up to 60 % of the dry mass) and low dry mass content (<5 %). For all samples compression and hold (relaxation after compression) data was collected and analyzed. The apparent Young's modulus of the mineralized beads was estimated by the Hertz model (compression data) and was shown to increase up to threefold upon mineralization. The enzymatically mineralized beads showed higher apparent Young's modulus compared to the ones mineralized by CD, even though the mineral content of the former was lower. Full compression-relaxation force-time profiles were analyzed using viscoelastic model. From this analysis, infinite and instantaneous Young's moduli were determined. Similarly, enzymatic mineralized beads, showed higher instantaneous and infinite Young's modulus, even if the degree of mineralization is lower then that achieved for CD method. This leads to the conclusion that both the degree of mineralization and the spatial distribution of mineral are important for the mechanical performance of the composite beads, which is in analogy to highly structured mineralized tissues found in many organisms.