<p>This paper mainly deals with the subresonance of vibration isolation systems with a bionic paw-inspired structure and offers an in-depth theoretical exploration of the subharmonic, ultra-subharmonic, and ultraharmonic resonances of those kinds of systems. The amplitude–frequency response and associated stability conditions are rigorously derived through the method of multiple scales. The theoretical analysis of the systems reveals different properties of the ultraharmonic, ultra-subharmonic, and subharmonic resonance. Ultra-subharmonic resonances of order less than 1 resemble the properties of subharmonic resonance, while those of order greater than 1 align more closely with the properties of ultraharmonic resonance. Reducing the excitation amplitude and increasing the damping coefficient both reduce the response amplitude. By integrating the isolation systems, time histories and frequency spectrums are obtained. Through the analysis of time histories, the results demonstrate a strong alignment with the theoretical predictions, confirming the accuracy and reliability of the theoretical framework. The frequency spectrum indicates that multiple subresonances are simultaneously generated in the steady-state response of the systems when certain parameters are chosen. It is demonstrated that by optimizing the structural parameters of the bionic vibration isolation structure, it is possible to mitigate the effects associated with subharmonic, ultra-subharmonic, and ultraharmonic resonances. The findings of this study lay a robust foundation for further research in physical and engineering vibration isolation.</p>