In vortex lasers, two modes with the same order but opposite chirality will be superposed in output. Therefore, we build a partially coherent superposition model for the two modes with opposite chirality and the same order, and investigate the superposition characteristics of the modes under continuous and passively Q-switched operation separately through experiments. Under a low-power pump, the modes coherently superpose to form petal-like light spots with the orientation determined by the initial phase difference under continuous operation. However, under Q-switched operation, the orientation of the petal-like light spots changes randomly with the pulse train. Under a high-power pump, the two modes superpose incoherently and present ring-shaped light spots without vortex phases, which is due to the random phase fluctuation caused by fierce mode competition. The mode chirality can be controlled by the tilted output mirror and the passive Q-switch to generate continuous vortex beams for the LG0,±1 modes, LG0,±2 modes, and LG0,±3 modes with the power of 0.88 W, 0.85 W, and 0.79 W, respectively, and LG0,±1 pulse vortex beam with a repetition rate of 12.6 kHz, a pulse width of 28.6 ns, and a peak power of 1.33 kW.