Three-dimensional (3D) printing now enables the fabrication of 3D structural electronics and microfluidics. Further, conventional subtractive manufacturing processes for microelectromechanical systems (MEMS) relatively limit device structure to two dimensions and require post-processing steps for interface with microfluidics. Thus, the objective of this work is to create an additive manufacturing approach for fabrication of 3D microfluidic-based MEMS devices that enables 3D configurations of electromechanical systems and simultaneous integration of microfluidics. Here, we demonstrate the ability to fabricate microfluidic-based acoustofluidic devices that contain orthogonal out-of-plane piezoelectric sensors and actuators using additive manufacturing. The devices were fabricated using a microextrusion 3D printing system that contained integrated pick-and-place functionality. Additively assembled materials and components included 3D printed epoxy, polydimethylsiloxane (PDMS), silver nanoparticles, and eutectic gallium-indium as well as robotically embedded piezoelectric chips (lead zirconate titanate (PZT)). Electrical impedance spectroscopy and finite element modeling studies showed the embedded PZT chips exhibited multiple resonant modes of varying mode shape over the 0-20 MHz frequency range. Flow visualization studies using neutrally buoyant particles (diameter = 0.8-70 μm) confirmed the 3D printed devices generated bulk acoustic waves (BAWs) capable of size-selective manipulation, trapping, and separation of suspended particles in droplets and microchannels. Flow visualization studies in a continuous flow format showed suspended particles could be moved toward or away from the walls of microfluidic channels based on selective actuation of in-plane or out-of-plane PZT chips. This work suggests additive manufacturing potentially provides new opportunities for the design and fabrication of acoustofluidic and microfluidic devices.