Recently, two-dimensional (2D) transition metal dichalcogenides with Janus structures, such as MoSSe, have been successfully synthesized through a two-step process involving hydrogenation followed by thermal selenization on a MoS2 monolayer, where the vertical dipole introduces a degree of freedom that enables the exploration of unusual optical properties. Incorporating both exciton and spin–orbit coupling (SOC) effects within the GW-BSE framework, however, remains a challenge, resulting in significant discrepancies between the theoretical prediction and the experimentally measured optical gap for the pristine MoSSe monolayer. In this paper, we utilize first-principles density functional theory combined with the many-body perturbation method, i.e., the GW-BSE method, to investigate strong exciton effects on the optical responses of 2D Janus MoSSe. For the pristine system, the vertical dipole moment attains a value of 390 e·μm, contrasting with nonpolar MoS2 and MoSe2 monolayers. The exciton-dominated optical gap of 1.70 eV aligns closely with the experimentally determined value of 1.68 eV. Our investigation into strain effects reveals that as the lattice constant increases, the vertical dipole moment increases from 360 e·μm under −4% strain to 400 e·μm under 4% strain. Simultaneously, both the global band gap and the direct band gap at the K point decrease. The optical gap monotonically increases from 1.3 to 2.1 eV, which is comparable to the tunable energy range of 0.8 eV found in MoS2 and MoSe2 monolayers and exceeds that of blue and Hittorf's phosphorenes. Regarding the SOC effect, the splitting between the A and B peaks shows an increasing trend, with a variation of 24 meV. This behavior can be employed for precise optical control, facilitating the development of optical modulators and demodulators. Together with the increasing lifetime and decreasing binding energy of excitons, the enhanced intrinsic dipole is expected to promote effective electron–hole separation, thereby enhancing the efficiency of photon-to-electricity conversion in this Janus structure.