Controlling spin current lies at the heart of spintronics and its applications. The sign of spin currents is monotonous in ferromagnets once the current direction is determined. Spin currents in antiferromagnets can possess opposite polarization, but requires enormous magnetic fields to lift the degeneracy. Controlling spin currents with different polarization is urgently demanded but remains hitherto elusive. Here, we demonstrate the control of spin currents at room temperature by magnon interference in a canted antiferromagnet, hematite recently also classified as an altermagnet. Magneto-optical characterization by Brillouin light scattering revealed that the spatial periodicity of the beating patterns was tunable via the microwave frequency. The inverse spin-Hall voltage changed sign as the frequency was scanned, i.e., a frequency-controlled switching of polarization in pure spin currents was obtained. Our work marks the use of antiferromagnetic magnon interference to control spin currents, which substantially extends the horizon for the emerging field of coherent antiferromagnetic spintronics.