Motivation: Phylogenetic reconstruction of tumor evolution has emerged as a crucial tool for making sense of the complexity of emerging cancer genomic datasets. Despite the growing use of phylogenetics in cancer studies, though, the field has only slowly adapted to many ways that tumor evolution differs from classic species evolution. One crucial question in that regard is how to handle inference of structural variations (SVs), which are a major mechanism of evolution in cancers but have been largely neglected in tumor phylogenetics to date, in part due to the challenges of reliably detecting and typing SVs and interpreting them phylogenetically. Results: We present a novel method for reconstructing evolutionary trajectories of SVs from bulk whole-genome sequence data via joint deconvolution and phylogenetics, to infer clonal sub-populations and reconstruct their ancestry. We establish a novel likelihood model for joint deconvolution and phylogenetic inference on bulk SV data and formulate an associated optimization algorithm. We demonstrate the approach to be efficient and accurate for realistic scenarios of SV mutation on simulated data. Application to breast cancer genomic data from The Cancer Genome Atlas shows it to be practical and effective at reconstructing features of SV-driven evolution in single tumors. Availability and implementation: Python source code and associated documentation are available at https://github.com/jaebird123/tusv.