Patients with pancreatic neuroendocrine tumors (PNET) commonly develop advanced disease and require systemic therapy. However, treatment options remain limited, in part, because experimental models that reliably emulate PNET disease are lacking. We therefore developed a patient-derived xenograft model of PNET (PDX-PNET), which we then used to evaluate two mTOR inhibitor drugs: FDA-approved everolimus and the investigational new drug sapanisertib. PDX-PNETs maintained a PNET morphology and PNET-specific gene expression signature with serial passage. PDX-PNETs also harbored mutations in genes previously associated with PNETs (such as MEN1 and PTEN), displayed activation of the mTOR pathway, and could be detected by Gallium-68 DOTATATE PET-CT. Treatment of PDX-PNETs with either everolimus or sapanisertib strongly inhibited growth. As seen in patients, some PDX-PNETs developed resistance to everolimus. However, sapanisertib, a more potent inhibitor of the mTOR pathway, caused tumor shrinkage in most everolimus-resistant tumors. Our PDX-PNET model is the first available, validated PDX model for PNET, and preclinical data from the use of this model suggest that sapanisertib may be an effective new treatment option for patients with PNET or everolimus-resistant PNET.