This paper presents an assessment model for the responsive capacity (RC) of an Electric Vehicle (EV) cluster, with a particular emphasis on the flexibility factors during charging and discharging processes, integrating it within a framework for grid interaction and control. A core concept of 'charging and discharging freedom' is introduced, which quantifies the response potential of EVs on both short-term and medium-to-long term scales. Further, utilizing travel chain rules, simulation models are developed to mimic the differentiated travel patterns of three typical EV user groups, ensuring the realism and accuracy of the analysis. Simulation outcomes demonstrate that, through optimized control, EV clusters can exhibit substantial flexibility to accommodate dynamic changes in power demand. The proposed control strategies effectively promote a balanced distribution of State-of-Charge (SOC) values, reducing instances of extreme high or low SOC, steering the controlled EV cluster's SOC distribution towards a more centralized profile, thereby enhancing the overall stability and efficiency of the system. These findings collectively validate, from both theoretical and practical perspectives, the efficacy of considering charging and discharging flexibility in assessing EV cluster response capabilities and optimizing control strategies.