Intrinsic spatial inhomogeneity or phase separation in cuprates, manganites, etc., related to electronic and/or magnetic properties, has attracted much attention due to its significance in fundamental physics and applications. Here we use scanning Kerr microscopy and scanning electron microscopy with polarization analysis with in situ electric fields to reveal the existence of intrinsic spatial inhomogeneity of the magnetic response to an electric field on a mesoscale with the coexistence of looplike (nonvolatile) and butterfly-like (volatile) behaviors in Co40Fe40B20/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 ferromagnetic/ferroelectric (FM/FE) multiferroic heterostructures. Both the experimental results and micromagnetic simulations suggest that these two behaviors come from the 109° and the 71°/180° FE domain switching, respectively, which have a spatial distribution. This FE domain-switching-controlled magnetism is significant for understanding the nature of FM/FE coupling on the mesoscale and provides a path for designing magnetoelectric devices through domain engineering.