General relativity interprets gravity as curvature of continuous spacetime manifold, where extreme perturbations solely generate propagating gravitational waves. Inspired by continuum mechanics that medium under violent impact produces both wave excitation and bulk fragmentation, this paper proposes the hypothesis of Localized Spacetime Fragments (LSFs) together with the cosmological sedimentation mechanism. Intense primordial matter loading in early universe breaks the intrinsic binding energy of spacetime fabric and peels off discrete geometric fragments decoupled from the bulk spacetime. Being free of electromagnetic interaction, LSFs contribute effective gravitational mass and provide a purely geometric explanation for dark matter. An extended gravitational Lagrangian including fragmentation potential is established, and the modified Einstein field equation with rigorous LSF stress-energy tensor is derived via variational principle. The cosmic production rate and abundance of LSFs are quantified, consistent with dark matter density measured by Planck CMB observation. The model is constrained by primordial nucleosynthesis, CMB non-Gaussian fluctuation and colliding galaxy cluster data. Furthermore, mild background spacetime fragmentation naturally accounts for cosmic dark energy, forming a self-consistent cosmological framework. Unique observable signatures including anomalous mass deficit during binary black hole mergers and small-scale structural deviations from ΛCDM are predicted for future astronomical verification.