Multi-functional two-dimensional (2D) materials are being researched due to their attractive properties and novel applications in nano-electronic, nano-optoelectronic, topological insulator, and energy-storage devices. In the present contribution, with the aid of first-principles calculations, the mechanical and nonlinear optical properties of a newly designed Be₂BO₃F₂ (BBF) monolayer were investigated. Our results illustrate that the BBF monolayer possesses unexpectedly higher flexibility than the typical and well-known flexible optoelectronic material MoS₂ in terms of Young's modulus. Moreover, the BBF monolayer also exhibits a strong second harmonic generation (SHG) response of 5.65 × 10⁴ pm² V⁻¹ which is 2.5 times that of a MoS₂ monolayer. The honeycomb structure of the BBF monolayer appears to have a good mechanical stability, as revealed by the positive phonon modes and elastic constants. The highlighted electronic structure and properties, such as the large band gap (7.95 eV) and the large SHG response, make the BBF monolayer suitable for potential applications in flexible deep ultra-violet (DUV) nonlinear optical devices. We believe that the present research will provide useful guidance for the design of a new generation of nano-electronic devices.