Considerable efforts have recently focused on sound vortices imprinted with orbital angular momentum (OAM) yet whose generation generally relies on sophisticated phase modulation, whether through traditional phased arrays or emerging metamaterial methods. Here, we propose and numerically demonstrate a mechanism for broadband generation of acoustic vortices in a simple, flexible, and high-efficiency way through binary-phase-based chirality modulation enabled by building a binary coding metasurface. The metasurface with a theoretically derived phase profile that is implemented with two types of meta-structures is capable of twisting the incident plane wave into a vortex beam with a desired order in a broad band and at the same time enables steering the vortices' propagation direction freewheelingly. The effectiveness of our proposed mechanism is verified by numerically demonstrating the broadband generation of vortex beams carrying different OAMs through a monolayered binary coding metasurface. We further demonstrate the generality and flexibility of our mechanism for generating the multiplexed vortex beams as well as modulating the propagation direction of the output beam by judiciously designing the 1-bit coding sequences of the metasurface. We anticipate our design with capability and simplicity to have far-reaching implications in OAM-enabled applications ranging from high-capacity acoustic communication to contactless particle manipulation.