This study proposes an elegant spatio-temporal compressed sensing scheme to significantly reduce the amount of data required to form quantitative acoustic microscopy (QAM) images. QAM systems form two-dimensional acoustic parameter maps of thin section of soft tissues. QAM data collection consists in raster scanning a sample in 2D and digitizing backscattered RF signals at each scan location. Therefore, the raw QAM data is three-dimensional and when using this conventional data acquisition process, data sets can be large causing processing and storage limitations. Our previous work demonstrated that the amount of QAM data can be remarkably reduced either spatially or temporally by using compressive sampling (CS) or finite rate of innovation (FRI) approaches, respectively. These approaches take advantage of the properties of QAM data, i.e., the sparsity of 2D maps and the parametric representation of RF signals. Therefore, in this study both approaches were combined into a single spatio-temporal solution. Results yielded a new data volume size of only 2.6% of the data originated by classical sampling techniques without significant deterioration of the 2D maps.