  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 {\em{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} SN kick. The
subsequent heating and acceleration of the evaporated star material along with
the SN ejecta by the magnetar wind can produce a post-peak bump in the SLSN
lightcurve. Our model can reproduce the primary peaks and post-peak bumps of
four example observed multiband SLSN lightcurves, revealing that the mass of
the evaporated material could be $\sim0.4-0.6\,M_\odot$ 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 post-peak
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.
