High-accuracy level underwater acoustical surveying plays an important role in ocean engineering applications, such as subaqueous tunnel construction, oil and gas exploration, and resources prospecting. This novel imaging method is eager to break through the existing theory to achieve a higher accuracy level of surveying. Multibeam Synthetic Aperture Sonar (MBSAS) is a kind of underwater acoustical imaging theory that can achieve 3D high-resolution detecting and overcome the disadvantages of traditional imaging methods, such as Multibeam Echo Sounder (MBES) and Synthetic Aperture Sonar (SAS). However, the resolution in the across-track direction inevitably decreases with increasing range, limited by the beamwidth of the transducer array of MBES. Furthermore, the sidelobe problem is also a significant interference of imaging sonar that introduces image noise and false peaks, which reduces the accuracy of the underwater images. Therefore, we proposed an accelerated deconvolved MBSAS beamforming method that introduces exponential acceleration and vector extrapolation to improve the convergence velocity of the classical Richardson-Lucy (R-L) iteration. The method proposed achieves a narrow beamwidth with a high sidelobe ratio in a few iterations. It can be applied to actual engineering applications, which breaks through the limitation of the actual transducer array scale. Simulations, tank, and field experiments also demonstrate the feasibility and advantages of the method proposed. 3D high-accuracy level underwater acoustical surveying can be achieved through this 2D MBES transducer array system, which can be widely promoted in the field of underwater acoustical remote sensing.