Terahertz vortex beams need to be developed for supporting new applications in fundamental sciences. In this paper, a novel and feasible scheme is presented for generation of helically microbunched electron beam for the emission of terahertz (THz) vortex pulses. In the scheme, a seed laser pulse with longitudinal and azimuthal modulation is firstly produced by optical beating of dual-vortex pulses. Through the laser-electron interaction, such a complex profile of laser can be converted to a periodically azimuth-dependence energy modulation in the electron beam, which finally forms a helical microbunching structure in the beam after a dispersion section. Then, this electron beam is applied to emit THz vortex beams and its quantum number can be continuously tuned by changing the topological charges of the optical laser pulses. This approach is suited to conventional accelerator system consisted of a modulator and a chicane. We expect this presentation can access to new researches in THz science.