In the present work, classical Molecular Dynamic simulations have been performed to peruse the effect of different grain sizes, temperatures and strain rates for different percentage of boron and nitrogen doping on the mechanical properties of polycrystalline graphene. Therefore, we studied 1%, 3%, 6% and 10% of boron or nitrogen doping for grain sizes of 1, 5, 10, 15, and 20 nm of graphene nanosheets at room temperature. The effect of different temperatures (100, 300, 600 and 900 K) on the mechanical response is investigated for five grain sizes (1, 5, 10, 15 and 20 nm) and 6% of boron or nitrogen doped polycrystalline graphene. Moreover, we studied different engineering strain rates on the mechanical response of six percentage of boron or nitrogen doped polycrystalline graphene for all simulation samples at 300 K. Our findings revealed that the mechanical response of polycrystalline graphene decrease as nitrogen or boron atoms are substituted into the nanosheet. By increasing of nitrogen atoms into polycrystalline graphene, a destructive affect occurs on the ultimate failure strain and tensile strength. Furthermore, the tensile strength tends to increase as the grain sizes increase from 1 to 20 nm. On the contrary, the failure strain has a tendency to decrease. As the temperatures increase in boron or nitrogen doped polycrystalline graphene, the tensile strength decreases as well as the failure strain. An increasing trend has been observed for mechanical properties of boron or nitrogen doped polycrystalline graphene as the strain rate increase. However, the effect of nitrogen on the tensile strength of nanosheet is more significant compared to boron doped nanosheet.