To obtain the mechanical energy of waves from arbitrary directions, the vibration absorbers of wave energy converters (WEC) are usually vertically axisymmetric. In such case, the wave-body interaction hydrodynamics is an essential research topic to obtain high-efficiency wave energy. In this paper, a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped stepped surfaces based upon the boundary approximation method (BAM) is introduced and examined. The hydrodynamic loads and parameters, such as the wave excitation forces, added mass and radiation damping of the vertical axisymmetric oscillating buoys, can then be achieved by using the new boundary discretisation method. The calculations of the wave forces and hydrodynamic coefficients show good convergence with the number of discretisation increases. Comparison between the constringent results and the results of the conventional method also verifies the feasibility of the method. Then, simulations and comparisons of the hydrodynamic forces, motions and wave power conversions of the buoys with series draught and displacement ratios in regular and irregular waves are conducted. The calculation results show that the geometrical shape has a great effect on the hydrodynamic and wave power conversion performance of the absorber. In regular waves, though the concave buoy has the lowest wave conversion efficiency, it has the largest frequency bandwidth for a given draught ratio, while in irregular waves, for a given draught ratio, the truncated cylindrical buoy has the best wave power conversion, and for a given displacement of the buoy, the concave buoy shows the best wave power conversion ability.