Acoustic vortices are intensely researched in metasurfaces for their potential application in acoustic communication and particle manipulation. By elaborately designing acoustic metasurfaces with phase profiles, an acoustic vortex is obtained. However, most existing studies are limited to the single working frequency and the specific topological charge. To address these limitations, a tunable broadband acoustic vortex generator is designed to generate acoustic vortices with multiple orders. For this purpose, an annulus subwavelength Mie resonator is theoretically proposed first. In the Mie resonator, the multipole mode is excited by coupling eccentric monopole sources at related resonance frequencies. Then coupling the Mie resonance structure and two eccentric monopole sources can realize the multipole crossing, thus generating acoustic vortices with topological charge m of ±1, ±2, ±3, ±4, and ±5. Numerical simulations and an experiment further confirm the theory. In addition, frequency tunability, broadband characteristics, and system robustness are quantitatively studied. The designed vortex generator performs well on these characteristics, which may have potential applications in acoustic communication for multiplexing and demultiplexing.