Circulating tumor cells (CTCs) from peripheral blood hold important information for cancer diagnosis and disease monitoring. Analysis of this "liquid biopsy" holds the promise to usher in a new era of personalized therapeutic treatments and real-time monitoring for cancer patients. But the extreme rarity of CTCs in blood makes their isolation and characterization technologically challenging. This paper reports the development of a geometrically enhanced mixing (GEM) chip for high-efficiency and high-purity tumor cell capture. We also successfully demonstrated the release and culture of the captured tumor cells, as well as the isolation of CTCs from cancer patients. The high-performance microchip is based on geometrically optimized micromixer structures, which enhance the transverse flow and flow folding, maximizing the interaction between CTCs and antibody-coated surfaces. With the optimized channel geometry and flow rate, the capture efficiency reached >90% with a purity of >84% when capturing spiked tumor cells in buffer. The system was further validated by isolating a wide range of spiked tumor cells (50-50,000) in 1 mL of lysed blood and whole blood. With the combination of trypsinization and high flow rate washing, captured tumor cells were efficiently released. The released cells were viable and able to proliferate, and showed no difference compared with intact cells that were not subjected to the capture and release process. Furthermore, we applied the device for detecting CTCs from metastatic pancreatic cancer patients' blood; and CTCs were found from 17 out of 18 samples (>94%). We also tested the potential utility of the device in monitoring the response to anti-cancer drug treatment in pancreatic cancer patients, and the CTC numbers correlated with the clinical computed tomograms (CT scans) of tumors. The presented technology shows great promise for accurate CTC enumeration, biological studies of CTCs and cancer metastasis, as well as for cancer diagnosis and treatment monitoring.