Traditional acoustic metamaterials are limited by their fixed structures, usually enabling only a single acoustic field manipulation function. To alter their acoustic field regulation performance, redesign and remanufacturing are required, which restricts the practical applications of acoustic metamaterials. Although acoustic metamaterials based on the moiré effect have provided a novel strategy for the dynamic manipulation of acoustic waves, the coupling effect between cascaded units can introduce significant additional phase delay, interfering with the precise manipulation of wavefront phase. To address this, we propose a cascadable exponentially graded acoustic metamaterial (EGAM) based on the space-coiling structure. Its key design is the exponential gradient of insert plate lengths, achieving smooth acoustic impedance transition and suppressing additional phase delay during cascading. When used individually, the metamaterial exhibits a low transmission coefficient; however, after cascading, the minimum sound pressure transmission coefficient exceeds 0.8, meeting the requirements of acoustic transmission. A single unit of the structure can achieve a full 0–360° phase adjustment, with the phase delay showing a linear correlation with the structural parameters. Even under broadband conditions, the structure maintains excellent phase manipulation capability and transmission performance. Compared with traditional space-coiling structures, the additional phase delay induced by the coupling effect between units during cascading is negligible. Leveraging this advantage of minimal additional phase delay, an abnormal refraction acoustic metamaterial with tunable refraction angles is designed by combining the Moiré effect. Verified through numerical simulations and experimental measurements, the refraction angle can be continuously tuned from 0° to 51°, with a maximum error of only 4% between the theoretical and simulation results. Furthermore, the same design strategy is employed to realize tunable acoustic focusing. By analyzing the error between the ideal phase distribution and the actual phase distribution of the cascaded structure, the horizontal coordinate of the focusing point is successfully shifted from 0–116 mm, with a maximum horizontal error of 2.6%. Both the tunable refraction angle and focusing position achieved in this work are in high consistency with the theoretical predictions. This study expands the application scope of reconfigurable acoustic metamaterials and provides a new perspective for multifunctional acoustic wave manipulation.