This paper presents the dynamic responses of sandwich beams with 3D printed thermoplastic composite face sheets and multi-walled carbon nanotubes reinforced magnetorheological elastomer (MWCNT-MR elastomer) cores under non-uniform magnetic fields. A higher-order beam theory (HoBT) is employed to express the beam‘s displacement field. The governing equations of the 3D printed thermoplastic sandwich beam are derived using Lagrange‘s principle and discretized by the finite element method. The validity of the present method is confirmed through comparison with the results available in the literature. The stiffness and damping characteristics of the 3D printed thermoplastic sandwich beam are investigated in relation to support conditions, non-homogeneous magnetic flux, and core-face sheet thickness ratio.