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In this work, density functional theory calculations were carried out to explore the mechanical response, dynamical/thermal stability, electronic/optical properties and photocatalytic features of monoclinic As2X3 (X=S, Se and Te) nanosheets. Acquired phonon dispersions and ab-initio molecular dynamics results confirm the stability of studied nanomembranes. Observation of relatively weak interlayer interactions suggests that the exfoliation techniques can be potentially employed to fabricate nanomembranes from their bulk counterparts. The studied nanosheets were found to show highly anisotropic mechanical properties. Notably, new As2Te3 2D lattice predicted by this study is found to exhibit unique superstretchability, which outperforms other 2D materials. In addition, our results on the basis of HSE06 functional reveal the indirect semiconducting electronic nature for the monolayer to few-layer and bulk structures of As2X3, in which a moderate decreasing trend in the band-gap by increasing the thickness can be established. The studied nanomaterials were found to show remarkably high and anisotropic carrier mobilities. Moreover, optical results show that these nanosheets can absorb the visible light. In particular, the valence and conduction band edge positions, high carrier mobilities and optical responses of As2Se3 nanosheets were found to be highly desirable for the solar water splitting. The comprehensive vision provided by this study not only confirm the stability and highly attractive electronic and optical characteristics of As2S3, As2Se3 and As2Te3 nanosheets, but also offer new possibilities to design superstretchable nanodevices.