Tissue dynamics spectroscopy uses digital holography as a coherence gate to extract depth-resolved quasi-elastic dynamic light scattering from inside multicellular tumor spheroids. The temporal speckle contrast provides endogenous dynamical images of proliferating and hypoxic or necrotic tissues. Fluctuation spectroscopy similar to diffusing wave spectroscopy is performed on the dynamic speckle to generate tissue-response spectrograms that track time-resolved changes in intracellular motility in response to environmental perturbations. The spectrograms consist of several frequency bands that range from 0.005 to 5 Hz. The fluctuation spectral density and temporal autocorrelations show the signature of constrained anomalous diffusion, but with large fluctuation amplitudes caused by active processes far from equilibrium. Differences in the tissue-response spectrograms between the proliferating outer shell and the hypoxic inner core differentiate normal from starved conditions. The differential spectrograms provide an initial library of tissue-response signatures to environmental conditions of temperature, osmolarity, pH, and serum growth factors.