We propose a method to generate specially shaped high-order singular beams of pre-designed intensity distributions. Such a method does not a priori assume a phase formula, but rather relies on the “cake-cutting and assembly” approach to achieve the azimuthal phase gradient for beam shaping, inspired by the orbital motion trajectory change of an artificial satellite. Based on our method, several typical vortex beams with desired intensity patterns are experimentally generated. As an example, we realize optical trapping and transportation of microorganisms with a triangle-shaped vortex beam, demonstrating the applicability of such unconventional vortex beams in optical trapping and manipulation.