Biopolymer-based composite hydrogels have attracted tremendous attention for tissue regeneration and antitumor applications. Since sodium alginate is a biopolymer, they offer excellent therapeutic options with long-term drug release and low side effects. To prepare multifunctional composite hydrogels with anticancer and tissue regeneration capabilities, sodium alginate (SA) and graphene oxide (GO) were covalently linked and crosslinked with tetraethyl orthosilicate (TEOS) by the solvothermal method. The structural and morphological results show that the hydrogels exhibit the desired functionality and porosity. The swelling of hydrogels in an aqueous and PBS medium was investigated. SGT-4 had the highest swelling in both aqueous and PBS media. Swelling and biodegradation of the hydrogel were inversely related. The drug release of SGT-4 was determined in different pH media (pH 6.4, 7.4, and 8.4) and the kinetics of drug release was determined according to the Higuchi model (R2 = 0.93587). Antibacterial activities were evaluated against severe infectious agents. Uppsala (U87) and osteoblast (MC3T3-E1) cell lines were used to determine the anticancer and biocompatibility of the composite hydrogels, respectively. These results suggest that the composite hydrogels could be used as potential biomaterials for tissue regeneration and antitumor applications.