Based on the first-principle calculation, we report a new kind of two-dimensional scandium oxyhalide monolayers. The formation energy, exfoliation energy, elastic constants, phonon spectra, molecular dynamic simulations, electronic structures, and optical properties were calculated. Analytical results confirmed that all the monolayers are energetically (with the exception of ScOF and ScOI), mechanically, dynamically, and thermally stable, and these monolayers are free-standing. The monolayers are widely indirect band gap semiconductors with band gaps obtained by the HSE06 scheme from 2.3 eV to 6.5 eV. The G0W0 plus the Bethe-Salpeter equation method reveals that ScOF, ScOCl, and ScOBr have large excitonic binding energies of 1.750, 1.123, and 0.622 eV, respectively. The high optical absorptions are observed in the UV light regions. Given their suitable band edges, large excitonic effects, and high optical absorptions in the UV light regions, ScOCl and ScOBr demonstrate great potential applications as photocatalysts for water splitting and solar-blind ultraviolet photodetectors.