Solar flares often involve the acceleration of particles to relativistic energies and the generation of high-intensity bursts of radio emission. In some cases, the radio bursts can show periodic or quasiperiodic intensity pulsations. However, precisely how these pulsations are generated is still subject to debate. Prominent theories employ mechanisms such as periodic magnetic reconnection, magnetohydrodynamic (MHD) oscillations, or some combination of both. Here we report on high-cadence (0.25 s) radio imaging of a 228 MHz radio source pulsating with a period of 2.3 s during a solar flare on 2014-April-18. The pulsating source is due to an MHD sausage mode oscillation periodically triggering electron acceleration in the corona. The periodic electron acceleration results in the modulation of a loss-cone instability, ultimately resulting in pulsating plasma emission. The results show that a complex combination of MHD oscillations and plasma instability modulation can lead to pulsating radio emission in astrophysical environments.