In this report, we successfully implement a unique cross-field beam deflector by exploiting the modulation of a one-dimensional refractive index in a copper-doped potassium tantalite niobite crystal. A theoretical model is established based on an electrostrictive effect regulated by the dynamic polarized nano-domains to explicate the mechanism of the abnormal beam deflection which is perpendicular to the applied electric field. Experimental results agree well with our theoretical deduction while validating the interactions between the dynamic polarized nano-domains and the applied electric field. Our findings will break the limitation of conventional electro-optic deflectors, paving the way to develop promising optical functional devices with a large field-of-view scanning angle and ultra-low driving voltage.