A scatter imaging technique for the differentiation of cancerous and healthy breast tissue in a heterogeneous sample is introduced in this work. Such a technique has potential utility in intraoperative margin assessment during lumpectomy procedures. In this work, we investigate the feasibility of the imaging method for tumor classification using Monte Carlo simulations and physical experiments. The coded aperture coherent scatter spectral imaging technique was used to reconstruct three-dimensional (3-D) images of breast tissue samples acquired through a single-position snapshot acquisition, without rotation as is required in coherent scatter computed tomography. We perform a quantitative assessment of the accuracy of the cancerous voxel classification using Monte Carlo simulations of the imaging system; describe our experimental implementation of coded aperture scatter imaging; show the reconstructed images of the breast tissue samples; and present segmentations of the 3-D images in order to identify the cancerous and healthy tissue in the samples. From the Monte Carlo simulations, we find that coded aperture scatter imaging is able to reconstruct images of the samples and identify the distribution of cancerous and healthy tissues (i.e., fibroglandular, adipose, or a mix of the two) inside them with a cancerous voxel identification sensitivity, specificity, and accuracy of 92.4%, 91.9%, and 92.0%, respectively. From the experimental results, we find that the technique is able to identify cancerous and healthy tissue samples and reconstruct differential coherent scatter cross sections that are highly correlated with those measured by other groups using x-ray diffraction. Coded aperture scatter imaging has the potential to provide scatter images that automatically differentiate cancerous and healthy tissue inside samples within a time on the order of a minute per slice.