Two-dimensional (2D) layered semiconductors with both ultrawide bandgap and strong second harmonic generation (SHG) are essential for expanding the nonlinear optical (NLO) applications to deep-ultraviolet (DUV) region in nanoscale. Unfortunately, these materials are rare in nature and have not been discovered until now. In this Letter, we predict the B2S2O9 (BSO), an existing layered oxide, can exhibit both DUV bandgap and strong SHG effects, comparable to the best known DUV NLO bulks. The strong SHG intensities in BSO, originated from the ordered arrangement of polar SO4 and BO4 tetrahedra forming planar structure, are linearly tunable by the layer thickness. Surprisingly, the spontaneous rotations of rigid tetrahedra under strains can induce the (nearly) zero Poissons ratios in BSO, which simultaneously result in the robust SHG effects against large strains, fundamentally differing from other known 2D NLO semiconductors. The discovery of BSO may provide an unprecedented opportunity to explore DUV NLO physics and applications in 2D limit.