We predict frequency multiplication of surface acoustic waves in dielectric substrates via the ferromagnetic resonance of adjacent magnetic transducers when driven by microwaves. We find pure second-harmonic generation (SHG) without any linear and third-harmonic components by a magnetic nanowire. The SHG and linear phonon pumping are switched by varying the saturated magnetization direction of the wire, or resolved directionally when pumped by a magnetic nanodisk. We address the high efficiency of SHG with comparable magnitude to that of the linear response, as well as a unique nonreciprocal phonon transport that is remarkably distinct in different phonon harmonics. Such an acoustic frequency comb driven by microwaves should bring exceptional tunability for miniaturized phononic and spintronic devices.