Two-dimensional (2D) MXenes are a rapid growing family of 2D materials with rich physical and chemical properties where their surface termination plays an essential role. Among the various 2D MXenes, function-alization of the TinCn-1 phase with oxygen (O) atoms makes them attractive for optoelectronic applications due to their optical gap residing in the infrared or visible region. In this paper, we theoretically investigate the electronic and optical properties of four different O-atom-functionalized TinCn-1 MXene monolayers using state-of-the-art, first-principles techniques. In particular, we calculate the quasiparticle corrections on top of density functional theory (DFT) with the GW approximation and the exciton-dominated optical spectra by solving the Bethe-Salpeter equation also at finite momentum. We find that all but one of the monolayer models are indirect band-gap semiconductors where quasiparticle corrections are very important (similar to 1 eV). The optical spectra are instead dominated by direct and indirect excitons with large binding energies (between 0.5 and 1 eV). Most direct excitons lie above 1.5 eV, while the indirect ones are below; therefore, we conclude that TinCn-1 should display strong absorption in the visible region, but phonon-assisted emission in the infrared. Our work thus reveals the potential usage of surface terminations to tune the optical and electronic properties of TinCn-1 MXene monolayers, while emphasizing the pivotal role of many-body effects beyond DFT to obtain accurate prediction for these systems.