Experimental observations of splitting of planar wave fronts propagating in a thin layer of Belousov-Zhabotinskii reaction mixture exposed to de electric field are described. Distinct effects of electric field on individual waves in a pattern can lead to a wave segmentation and development of disordered spatiotemporal structures via process of wave breakup and fusion. Stabilizing or destabilizing effects of electric field on free ends of wave segments are discussed in the frame of anisotropic and nonhomogeneous distribution of the medium’s refractoriness. Effects of electric field on circular waves are investigated numerically using a realistic scheme of the BZ reaction. Wave splitting, reversal, and annihilation that occur on the arcs of circular waves expanding toward the negative electrode are shown to depend both on the field intensity and on the wave order in a pattern.