Herein, we employed linear-response time-dependent functional theory nonadiabatic dynamic simulations to explore the photoinduced exciton dynamics of a chiral single-walled carbon nanotube CNT(6,5) covalently doped with a 4-nitrobenzyl group (CNT65-NO2). The results indicate that the introduction of a sp3 defect leads to the splitting of the degenerate VBM/VBM-1 and CBM/CBM+1 states. Both the VBM upshift and the CBM downshift are responsible for the experimentally observed redshifted E11* trapping state. The simulations reveal that the photoinduced exciton relaxation dynamics completes within 500 fs, which is consistent with the experimental work. On the other hand, we also conducted the nonadiabatic carrier (electron and hole) dynamic simulations, which completely ignore the excitonic effects. The comparison demonstrates that excitonic effects are indispensable. Deep analyses show that such effects induce several dark states, which play an important role in regulating the photoinduced dynamics of CNT65-NO2. The present work demonstrates the importance of including excitonic effects in simulating photoinduced processes of carbon nanotubes. In addition, it not only rationalizes previous experiments but also provides valuable insights that will help in the future rational design of novel covalently doped carbon nanotubes with superior photoluminescent properties.