We develop a novel unsupervised deconvolution method, within a well-grounded mathematical framework, to dissect mixed gene expressions in heterogeneous tumor samples. We implement an R package, UNsupervised DecOnvolution (UNDO), that can be used to automatically detect cell-specific marker genes (MGs) located on the scatter radii of mixed gene expressions, estimate cellular proportions in each sample and deconvolute mixed expressions into cell-specific expression profiles. We demonstrate the performance of UNDO over a wide range of tumor-stroma mixing proportions, validate UNDO on various biologically mixed benchmark gene expression datasets and further estimate tumor purity in TCGA/CPTAC datasets. The highly accurate deconvolution results obtained suggest not only the existence of cell-specific MGs but also UNDOs ability to detect them blindly and correctly. Although the principal application here involves microarray gene expressions, our methodology can be readily applied to other types of quantitative molecular profiling data.