Nonlinear vibration absorbers provide an effective alternative for energy dissipation in mechanical systems subjected to dynamic excitations. This study focuses on the analysis of the dynamic behavior of a two-degree-of-freedom system incorporating a nonlinear absorber with mechanical stops. A nonlinear mathematical model was developed by integrating regularized contact forces to capture the effects induced by the mechanical clearance between the absorber mass and the stops. Numerical simulations were conducted to investigate the system’s response to harmonic excitation. The results reveal three main findings: (1) a small clearance of 0.5 mm induces significant nonlinear effects, including a frequency shift; (2) this interaction contributes to a notable reduction in vibration amplitudes, especially near the second resonance; (3) the energy pumping phenomenon is enhanced, thus improving the efficiency of vibration absorption compared to conventional linear devices. These findings provide practical guidelines for designing high-performance nonlinear absorbers by leveraging mechanical clearance effects in industrial vibration control applications.