Controlling the spin current lies at the heart of spintronics and its applications. In ferromagnets, the sign of spin currents is fixed once the current direction is determined. However, spin currents in antiferromagnets can possess opposite polarizations, but this requires enormous magnetic fields to lift the degeneracy between the two modes. Therefore, controlling spin currents with opposite polarization is still a challenge. Here we demonstrate the control of spin currents at room temperature by magnon interference in a canted antiferromagnet, namely, haematite that has recently been classified as an altermagnet. Magneto-optical characterization by Brillouin light scattering reveals that the spatial periodicity of the beating patterns is tunable via the microwave frequency. We further observe that the inverse spin Hall voltage changes sign as the frequency is tuned, evincing a frequency-controlled switching of polarization of pure spin currents. Our work highlights the use of antiferromagnetic magnon interference to control spin currents, which substantially extends the horizon for the emerging field of coherent antiferromagnetic spintronics.