In this article, the impact of external constant and uniform magnetic field is investigated on the mixing efficiency and also geometric and dynamic characteristics of two-dimensional isotropic MHD flow. For this purpose, the direct numerical simulation (DNS) is applied to two-dimensional incompressible magneto-hydrodynamic equations by pseudo-spectral method. Calculations show that external magnetic field causes deformation of vortexes and this deformation is increased by intensification of magnetic field. The dynamic characteristics of flow are affected by these deformations. Investigation of mixing efficiency shows that increase in magnitude of magnetic field or decrease in magnetic diffusivity coefficient causes mixing efficiency to reduce. For explore of the factors affecting on mixing reduction, small and large scale vortexes are studied. Investigation of external magnetic field effect on dissipated energy rate that is associated with changes in the dynamics of small vortexes shows that viscose dissipated energy rate is reduced in the presence of magnetic field compared to its absence. However results show that total dissipated energy rate is increased compared to no magnetic field presence. In order to demonstrate of large scale vertex dynamics, total kinematic and magnetic energy are considered. It is shown that in the presence of external magnetic field, energy is transferred from flow field to magnetic field due to Lorentz force that both leads to reduction of mixing efficiency.