In this article, a novel bio-nanocomposite consists of sodium alginate polymer-based graphene nanosheet enhanced incorporating wollastonite containing various amount of graphene nanosheet were produced using freeze-drying technique. The bio-nanocomposites were mechanically and biologically evaluated using tensile strength and biological test. The phase and topological characterization were conducted using scanning electron microscopy (SEM) and X-ray diffraction (XRD) technique. Subsequently, based upon Euler-Bernoulli and Timoshenko beam theories (EBT and TBT), the buckling responses of the porous bio-nanocomposite soft tissue are analyzed corresponding to various graphene amounts. In order to solve the governing equations a sufficient numerical solution is proposed. Elastic modulus and mass density of the porous bio-nanocomposite are extracted from the experimental tests. The obtained results indicated the sample with 1 wt% graphene sheet has shown proper mechanical and biological features. Therefore, the sample with 1 wt% graphene sheet can be used as potential case for light weight bone substitute applications.