In this work, the structural, electronic and mechanical properties of fluorinated diamane (F-diamane) with N and B dopants are systemically investigated using first-principles calculation. The N atom tends to stay in the external substituted site without F saturation, while the B-doped structure of the substituted external site with F saturation is the most stable. Ab initio molecular dynamics simulations confirm the thermal stability. The band structures of stable doped structures are similar to that of pristine F-diamane, due to the slight contribution of the dopant to the band edges. In addition, after the introduction of the B dopant, the formation energy reduces, and the transition barrier of graphene bilayers into diamane is smaller, indicating the feasibility of graphene bilayer fluoridation. Furthermore, we find that these doped structures have mechanical stability with isotropic elastic constants, Young's modulus, shear modulus and Poisson's ratio. Our work would promote the synthesis and development of two-dimensional diamane.