The online precision mass spectrometer ISOLTRAP at ISOLDE/CERN was recently upgraded by adding a multi-reflection time-of-flight mass separator/ spectrometer (MR-ToF MS) between the linear radio-frequency ion trap and the two Penning traps already in place. As a mass separator, the MR-ToF device has improved significantly ISOLTRAP's capability of purification of contaminated ion beams. In addition, the MR-ToF MS can be operated as a mass spectrometer, either to analyze the ISOLDE ion beam or for precision mass measurements of nuclides that are shorter-lived or that have lower yields than those accessible for Penning-trap mass spectrometry. The MR-ToF MS and corresponding components, its integration into ISOLTRAP, and its various operation modes are reviewed. Furthermore, a precision measurement of the ¹³⁷Eu mass is presented, determined with the help of the MR-ToF device as a mass separator.