Bone tissue engineering offers an alternative approach to producing scaffolds using biodegradable materials. The extracellular matrix of bone tissue comprises collagen and hydroxyapatite so that regenerated scaffolds can be a combination of polymeric materials and hydroxyapatite. Additives are also used to improve the properties and bring the properties of the regenerated scaffold closer to bone tissue. This study focuses on developing nanocomposite scaffolds composed of natural polymers carboxymethyl cellulose (CMC) and alginate (Alg), combined with the synthetic polymer polyvinyl alcohol (PVA) as the polymer matrix. The mechanical properties of these biopolymers were enhanced using magnetic clay nanoparticles modified with graphene oxide (CGF) and natural hydroxyapatite (HAp). Modified clay was synthesized by adding graphene oxide (via the modified Hummer's method), clay, and Fe3O4 nanoparticles. Nanocomposite scaffolds were prepared using the freeze-drying process, incorporating 10 wt. % HAp and 2 wt. % CGF as optimal additives. Comprehensive characterization, including XRD, FT-IR, TGA, SEM, and analysis of porosity, swelling, degradation, and biomineralization, confirmed the formation of a porous polymer matrix with favorable properties. The optimal PVA/CMC/HAp/CGF scaffold demonstrated compressive strength of 12 MPa, porosity of 72%, swelling of 1860%, and biodegradation of 43% over 21 days, while the PVA/Alg/HAp/CGF scaffold exhibited a compressive strength of 8.1 MPa and porosity of 79%. Both scaffolds showed good biomineralization in SBF and a favorable cell viability rate (OD) in MTT toxicity tests, with an OD of 1.483 and 1.451 for PVA/CMC/HAp/CGF and PVA/Alg/HAp/CGF scaffolds, respectively. These findings suggest that the PVA/CMC/HAp/CGF nanocomposite scaffold is a promising candidate for bone tissue engineering applications. By adding hydroxyapatite and magnetic clay modified with graphene oxide to the polymer scaffold, the mechanical properties of the scaffold are increased, appropriate porosity and swelling values are obtained, and desirable cell viability is achieved.