The operational bandwidth of a cholesteric liquid crystal deflector based on the Bragg-Berry effect is analyzed using the two-dimensional finite-difference time-domain method. Despite its similarity in structure with a conventional cholesteric mirror under oblique incidence, the bandwidths of selective reflection and selective diffraction are different. The selective reflection wavelength from the cholesteric mirror has a cosine dependence on the Bragg angle, while that of selective diffraction from the cholesteric deflector has a cosine-squared dependence on the slant angle. We also propose equations that approximate the selective diffraction bandwidth of the deflector. The equations can be used to find the helical pitch required to achieve a deflector with a specified deflection angle and operational wavelength, thereby facilitating the development of cholesteric liquid crustal based diffractive optical elements.