Genuine quantum-mechanical effects are readily observable in modern optomechanical systems comprising “classical” (bosonic) optical resonators. Unique features and advantages of optical two-level systems (qubits) for optomechanics, however, have not been so thoroughly explored. We experimentally demonstrate these advantages using charge-controlled InAs quantum dots (QDs) in surface-acoustic-wave resonators. We coherently control QD population dynamics using engineered optical pulses and mechanical motion, i.e., using both phonons and photons. As a first example, at moderate acoustic drive strengths, we demonstrate the potential of this technique to maximize fidelity in quantum microwave-to-optical transduction. Specifically, the scheme is tailored to enhance mechanically assisted photon scattering over the direct detuned photon scattering from the QD. Spectral analysis reveals distinct scattering channels related to Rayleigh scattering and luminescence in our pulsed excitation measurements, which lead to time-dependent scattering spectra. Quantum-mechanical calculations show good agreement with our experimental results, together providing a comprehensive description of excitation, scattering, and emission in a coupled QD-phonon system. These results highlight unique opportunities to expand the functionality of quantum optomechanical systems.