Semiconducting single-walled carbon nanotubes (SWNTs) are one of the most intriguing nanomaterials due to their large aspect ratios, size tunable properties, and dominant many body interactions. While the dynamics of exciton population relaxation have been well characterized, optical dephasing processes have only been examined indirectly through steady-state measurements such as single-molecule spectroscopy that can yield highly variable estimates of the homogeneous linewidth. To bring clarity to these conflicting estimates, a time-domain measurement of exciton dephasing at an ensemble level is necessary. Using two-pulse photon echo (2PE) spectroscopy, comparatively long dephasing times approaching 200 fs are extracted for the (6,5) tube species at room temperature. In this contribution, we extend our previous study of 2PE and pump-probe spectroscopy to low temperatures to investigate inelastic exciton-exciton scattering. In contrast to the population kinetics observed upon excitation of the second transition-allowed excitonic state (E22), our one-color pump-probe data instead shows faster relaxation upon cooling to 60 K when the lowest transition-allowed state (E11) is directly excited for the (6,5) tube species. Analysis of the kinetics obtained suggests that the observed acceleration of kinetic decay at low temperature originates from an increasing rate of exciton-exciton annihilation. In order to directly probe exciton-exciton scattering processes, femtosecond 2PE signal is measured as a function of excitation fluence and temperature. Consistent with the observed enhancement of exciton-exciton scattering and annihilation at low temperatures, the dephasing rates show a correlated trend with the temperature dependence of the population lifetimes extracted from one-color pump-probe measurements.