We present a novel geometric theory in which dark matter and dark energy arise not from exotic particles or modifications of general relativity, but from topological defects—spacetime fragments—generated by the breakdown of the spacetime continuum. We introduce a concrete effective field theory where an extended Einstein-Hilbert action includes a quadratic curvature term (the Kretschmann scalar) that captures both intense, localized fragmentation (dark matter) and a residual background of diffuse micro‑fractures (dark energy). From this action we derive the modified Einstein field equations and the explicit form of the effective stress‑energy tensor for Local Spacetime Fragments (LSFs). Fragmentation is triggered when the local Kretschmann scalar exceeds a critical threshold \mathcal{R}_c defined by a spacetime binding energy scale. Crucially, dark energy is not produced by ongoing low‑curvature fragmentation; rather, it arises as the late‑time remnant of early‑universe fragmentation, analogous to residual stresses in a deformed elastic medium. The model naturally explains the Bullet Cluster decoupling, alleviates the Hubble tension via a time‑dependent effective dark energy density, and matches Planck CMB power spectra. We prove that gravitational waves propagate at exactly the speed of light at observable frequencies, satisfying the GW170817 constraint. We further derive a quantitative prediction for an anomalous mass deficit in binary black hole mergers, \Delta M_{\text{ano}} = \beta \left( \frac{M_{\text{BH}}}{M_{\text{Pl}}} \right)^2 M_{\text{Pl}} with \beta \sim 0.01-0.1, which is falsifiable with next‑generation gravitational wave detectors. The self‑interaction cross‑section of LSFs is computed and shown to be well within the Bullet Cluster bound. We also provide fits to dwarf galaxy rotation curves (e.g., NGC 6822) and a quantitative comparison of H_0 values, demonstrating consistency with observations while remaining distinct from \LambdaCDM and MOND.