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Wolf–Rayet stars in close binary systems can be tidally spun up by their companions, potentially leaving behind fast-spinning, highly magnetized neutron stars, known as “magnetars,” after core collapse. These newborn magnetars can transfer rotational energy into heating and accelerating the ejecta, producing hydrogen-poor superluminous supernovae (SLSNe). In this Letter, we propose that the magnetar wind of the newborn magnetar could significantly evaporate its companion star, typically a main-sequence or helium star, if the binary system is not disrupted by the abrupt mass loss and supernova (SN) kick. The subsequent heating and acceleration of the evaporated star material along with the SN ejecta by the magnetar wind can produce a postpeak bump in the SLSN lightcurve. Our model can reproduce the primary peaks and postpeak bumps of four example observed multiband SLSN lightcurves, revealing that the mass of the evaporated material could be ∼0.4–0.6 M _⊙ if the material is hydrogen-rich. We propose that the magnetar could induce strongly enhanced evaporation from its companion star near the pericenter if the orbit of the post-SN binary is highly eccentric, ultimately generating multiple postpeak bumps in the SLSN lightcurves. This “magnetar–star binary engine” model may offer a possible explanation for the evolution of polarization, along with the origin and velocity broadening of late-time hydrogen or helium broad spectral features observed in some bumpy SLSNe. The diversity in the lightcurves and spectra of SLSNe may be attributed to the wide variety of companion stars and post-SN binary systems.