Revealing the clonal composition of a single tumor is essential for identifying cell subpopulations with metastatic potential in primary tumors or with resistance to therapies in metastatic tumors. Sequencing technologies provide only an overview of the aggregate of numerous cells. Computational approaches to de-mix a collective signal composed of the aberrations of a mixed cell population of a tumor sample into its individual components are not available. We propose an evolutionary framework for deconvolving data from a single genome-wide experiment to infer the composition, abundance and evolutionary paths of the underlying cell subpopulations of a tumor. We have developed an algorithm (TrAp) for solving this mixture problem. In silico analyses show that TrAp correctly deconvolves mixed subpopulations when the number of subpopulations and the measurement errors are moderate. We demonstrate the applicability of the method using tumor karyotypes and somatic hypermutation data sets. We applied TrAp to Exome-Seq experiment of a renal cell carcinoma tumor sample and compared the mutational profile of the inferred subpopulations to the mutational profiles of single cells of the same tumor. Finally, we deconvolve sequencing data from eight acute myeloid leukemia patients and three distinct metastases of one melanoma patient to exhibit the evolutionary relationships of their subpopulations.