Temporal and spatial resonant modes are always possessed in physical systems with energy oscillation. In ultrafast fiber lasers, enormous progress has been made toward controlling the interactions of many longitudinal modes, which results in temporally mode-locked pulses. Recently, optical vortex beams have been extensively investigated due to their quantized orbital angular momentum, spatially donut-like intensity, and spiral phase front. In this paper, we have demonstrated the first to our knowledge observation of optical vortex mode switching and their corresponding pulse evolution dynamics in a narrow-linewidth mode-locked fiber laser. The spatial mode switching is achieved by incorporating a dual-resonant acousto-optic mode converter in the vortex mode-locked fiber laser. The vortex mode-switching dynamics have four stages, including quiet-down, relaxation oscillation, quasi mode-locking, and energy recovery prior to the stable mode-locking of another vortex mode. The evolution dynamics of the wavelength shifting during the switching process are observed via the time-stretch dispersion Fourier transform method. The spatial mode competition through optical nonlinearity induces energy fluctuation on the time scale of ultrashort pulses, which plays an essential role in the mode-switching dynamic process. The results have great implications in the study of spatial mode-locking mechanisms and ultrashort laser applications.