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Microscopic two-level system (TLS) defects at dielectric surfaces and interfaces are among the dominant sources of loss in superconducting quantum circuits, and their properties have been extensively probed using superconducting resonators and qubits. We report on spectroscopy of TLSs coupling to the strain field in a surface acoustic wave (SAW) resonator. The narrow free spectral range of the resonator allows for two-tone spectroscopy where a strong pump is applied at one resonance while a weak signal is used to probe a different mode. We map the spectral hole burnt by the pump tone as a function of frequency and extract parameters of the TLS ensemble. Our results suggest that detuned acoustic pumping can be used to enhance the coherence of superconducting devices by saturating TLSs.