Reservoir rocks of the Pearl River Mouth Basin’s Lufeng Sag have low porosity (average porosity 12.6%) and low permeability (average permeability 16.5 mD), requiring hydraulic fracturing to obtain economic production of oil and gas. To contribute to the understanding of these reservoirs, and to promote successful production in the region, we analyzed the mechanical properties of tight sandstone. Moreover, we introduced the shear/tensile strength factor, in combination with the fracture toughness and horizontal stress difference coefficient, as an innovative approach to characterize the ease of forming a complex fracture network after reservoir fracturing. Based on this, we established a fracability evaluation model suitable for offshore low-permeability sandstone reservoirs by an analytic hierarchy process from the perspective of whether the reservoir can form an effective transformation volume and complex fracture network after fracturing. The results indicate that the primary minerals of the target reservoir are quartz and clay minerals, and the natural fractures are not developed. The mechanical properties exhibit a high Young’s modulus (ranging from 30.4 to 34.4 GPa) and high compressive strength (with cohesion between 41 and 45 MPa and an angle of internal friction between 31.0 and 33.5°). The relatively low tensile strength and fracture toughness values are conducive to fracture initiation and extension during the fracturing process. Through the fracability evaluation model constructed in this paper, the depth interval at 4155.1–4172.1 m is identified as a high-quality fractured layer. The results of this study not only provide theoretical guidance for target well and formation selection in the Lufeng Sag, but also have important practical implications for increasing oil and gas production from tight sandstone reservoirs.