This work constitutes Block II (Dynamics) of a multi-part theoretical framework describing a vacuum with finite response capacity and intrinsic relaxation time. We develop the full nonlinear dynamics of a saturable scalar field, showing how bounded kinetic response leads to causal propagation, suppression of divergences, and regime-dependent behavior without introducing additional degrees of freedom. The theory naturally incorporates memory effects, finite relaxation scales, and nonlinear saturation, while preserving hyperbolicity and stability. Unlike standard treatments that assume instantaneous vacuum response, the present framework demonstrates that finite relaxation and capacity constraints are dynamically consistent and lead to well-defined evolution equations across excitation regimes. This block focuses exclusively on dynamical structure and evolution, providing the mathematical backbone required for subsequent analyses of microscopic consistency and large-scale phenomenology. No cosmological fitting or biological interpretation is introduced here. The framework is explicitly falsifiable and does not rely on post-hoc adjustments, positioning finite-capacity dynamics as a viable extension of standard field-theoretic descriptions.