Context. The latest evolutionary phases of low- and intermediate-mass stars are characterized by complex physical processes like turbulence, convection, stellar pulsations, magnetic fields, condensation of solid particles, and the formation of massive outflows that inject freshly produced heavy elements and dust particles into the interstellar medium. Aims. By investigating individual objects in detail, we wish to analyze and disentangle the effects of the interrelated physical processes on the structure of the wind-forming regions around them. Methods. We use the Northern Extended Millimeter Array to obtain spatially and spectrally resolved observations of the semi-regular asymptotic giant branch (AGB) star RS Cancri and apply detailed 3D reconstruction modeling and local thermodynamic equilibrium radiative transfer calculations in order to shed light on the morpho-kinematic structure of its inner, wind-forming environment. Results. We detect 32 lines of 13 molecules and isotopologs (CO, SiO, SO, SO2, H2O, HCN, PN), including several transitions from vibrationally excited states. HCN, H13CN, and millimeter vibrationally excited H2O, SO, 34SO, SO2, and PN are detected for the first time in RS Cnc. Evidence for rotation is seen in HCN, SO, SO2, and SiO(v = 1). From CO and SiO channel maps, we find an inner, equatorial density enhancement, and a bipolar outflow structure with a mass-loss rate of 1 × 10−7 M⊙yr−1 for the equatorial region and of 2 × 10−7 M⊙yr−1 for the polar outflows. The 12CO/13CO ratio is measured to be ~20 on average, 24 ± 2 in the polar outflows and 19 ± 3 in the equatorial region. We do not find direct evidence of a companion that might explain this kind of kinematic structure, and explore the possibility that a magnetic field might be the cause of it. The innermost molecular gas is influenced by stellar pulsation and possibly by convective cells that leave their imprint on broad wings of certain molecular lines, such as SiO and SO. Conclusions. RS Cnc is one of the few nearby, low-mass-loss-rate, oxygen-rich AGB stars with a wind displaying both an equatorial disk and bipolar outflows. Its orientation with respect to the line of sight is particularly favorable for a reliable study of its morpho-kinematics. Nevertheless, the mechanism causing early spherical symmetry breaking remains uncertain, calling for additional high spatial- and spectral-resolution observations of the emission of different molecules in different transitions, along with more thorough investigation of the coupling among the different physical processes at play.