Three-dimensional (3D) ultrasound (US) imaging addresses the limitation in field-of-view (FOV) in conventional two-dimensional (2D) US imaging by providing 3D viewing of the anatomy. 3D US imaging has been extensively adapted for diagnosis and image-guided surgical intervention. However, conventional approaches to implement 3D US imaging require either expensive and sophisticated 2D array transducers, or external actuation mechanisms to move a one-dimensional array mechanically. Here, we propose a 3D US imaging mechanism using actuated acoustic reflector instead of the sensor elements for volume acquisition with significantly extended 3D FOV, which can be implemented with simple hardware and compact size. To improve image quality on the elevation plane, we introduce an adaptive-delay synthetic aperture focusing (AD-SAF) method for elevation beamforming. We first evaluated the proposed imaging mechanism and AD-SAF with simulated point targets and cysts targets. Results of point targets suggested improved image quality on the elevation plane, and results of cysts targets demonstrated a potential to improve 3D visualization of human anatomy. We built a prototype imaging system that has a 3D FOV of 38 mm (lateral) by 38 mm (elevation) by 50 mm (axial) and collected data in imaging experiments with phantoms. Experimental data showed consistency with simulation results. The AD-SAF method enhanced quantifying the cyst volume size in the breast mimicking phantom compared to without elevation beamforming. These results suggested that the proposed 3D US imaging mechanism could potentially be applied in clinical scenarios.