The auto-recloser (AR) contributes to the service restoration of the transmission lines tripped by overload and relay protection mal-operation, which may complicate cascading outage processes. This brief develops a novel model to investigate the impact of ARs on cascading failure (CF) propagation in power systems with the representation of temporal evolution. The cascading outage processes with and without ARs are first compared in a timeline manner to highlight the function of ARs. Then, combined with the inverse time and hidden failure characteristics of overcurrent protections, the CF model considering ARs is established to elaborate the cascading propagation and reveal the reclosing effect. Finally, the time-constrained optimal dispatching strategy is proposed to block CFs in time before the next line excision. Case studies on IEEE 118-bus and IEEE 300-bus systems demonstrate the feasibility and effectiveness of the proposed method.