Twinning stress is known to be a critical factor for the actuating performance of magnetic shape memory alloys because of the harmful deterioration of their magnetic field-induced strain effect. However, the intrinsic origin of the high twinning stress is still in debate. In this work, we firstly fill this gap by precisely probing the reorientation behaviors of A-C and A-B two common macro-twin interfaces under the stimulus of uniaxial compression in-situ transmission electron microscope. The grain boundary is proved to be the main reason for large twinning stress. The twinning stress of the A-C and A-B type interfaces quantitatively are ∼0.69 and 1.27 MPa within the plate respectively. The A-C type interface evidently has smaller twinning stress and larger deformation variable than the A-B interface. Under the action of compression, not only the orientations of the crystals have changed, but also the roles of the major and minor lamellae have changed for both interfaces due to the movements of twinning dislocations. Combining in-situ and quasi in-situ electron diffraction data, the reorientation process is clearly and intuitively shown by the stereographic projection. Atomic models and the theory of dislocation motion are proposed to phenomenologically clarify the intrinsic mechanism. This work is believed to not only provide a deeper understanding of the deformation mechanism of magnetic shape memory alloys under uniaxial compression testing, but also discover that compression training is not the mechanical training way to decrease the twinning stress of non-modulated martensite in single crystal shape memory alloys.