Flexoelectricity is an electromechanical coupling between electrical polarization and a strain gradient(1) that enables mechanical manipulation of polarization without applying an electrical bias(2,3). Recently, flexoelectricity was directly demonstrated by mechanically switching the out-of-plane polarization of a uniaxial system with a scanning probe microscope tip(3,4). However, the successful application of flexoelectricity in low-symmetry multiaxial ferroelectrics and therefore active manipulation of multiple domains via flexoelectricity have not yet been achieved. Here, we demonstrate that the symmetry-breaking flexoelectricity offers a powerful route for the selective control of multiple domain switching pathways in multiaxial ferroelectric materials. Specifically, we use a trailing flexoelectric field that is created by the motion of a mechanically loaded scanning probe microscope tip. By controlling the SPM scan direction, we can deterministically select either stable 71 degrees ferroelastic switching or 180 degrees ferroelectric switching in a multiferroic magnetoelectric BiFeO3 thin film. Phase-field simulations reveal that the amplified in-plane trailing flexoelectric field is essential for this domain engineering. Moreover, we show that mechanically switched domains have a good retention property. This work opens a new avenue for the deterministic selection of nanoscale ferroelectric domains in low-symmetry materials for non-volatile magnetoelectric devices and multilevel data storage.