We formalize the Spacetime Exclusion Principle (SEP), originally introduced in Naik (2026), as a foundational constraint on gravitational physics. By defining time operationally via entropy progression and imposing distinguishability as a prerequisite for physical meaning, we demonstrate that spacetime admits a finite capacity to organize degrees of freedom. We prove that gravitational strength is necessarily bounded and that classical spacetime structure cannot exist beyond saturation surfaces such as black hole event horizons. A modified action principle implementing SEP is constructed, and we show that classical general relativity violates operational distinguishability beyond horizons by extending manifold structure where no measurement is possible. Singularities, baby universes, and interior spacetime continuations are excluded without modifying Einstein dynamics within their validated domain.