Cancer genetics has to date focused on epithelial malignancies, identifying multiple histotype-specific pathways underlying cancer susceptibility. Sarcomas are rare malignancies predominantly derived from embryonic mesoderm. To identify pathways specific to mesenchymal cancers, we performed whole-genome germline sequencing on 1644 sporadic cases and 3205 matched healthy elderly controls. Using an extreme phenotype design, a combined rare-variant burden and ontologic analysis identified two sarcoma-specific pathways involved in mitotic and telomere functions. Variants in centrosome genes are linked to malignant peripheral nerve sheath and gastrointestinal stromal tumors, whereas heritable defects in the shelterin complex link susceptibility to sarcoma, melanoma, and thyroid cancers. These studies indicate a specific role for heritable defects in mitotic and telomere biology in risk of sarcomas.