We describe an apparatus for investigating the excited-state dissociation dynamics of mass-selected ion-molecule clusters by mass-resolving and detecting photofragment-ions and neutrals, in coincidence, using an ultrafast laser operating at high repetition rates. The apparatus comprises a source that generates ion-molecule clusters, a time-of-flight spectrometer, and a mass filter that selects the desired anions, and a linear-plus-quadratic reflectron mass spectrometer that discriminates the fragment anions after the femtosecond laser excites the clusters. The fragment neutrals and anions are then captured by two channeltron detectors. The apparatus performance is tested by measuring the photofragments: I-, CF3I-, and neutrals from photoexcitation of the ion-molecule cluster CF3I·I- using femtosecond UV laser pulses with a wavelength of 266 nm. The experimental results are compared with our ground state and excited state electronic structure calculations as well as the existing results and calculations, with particular attention to the generation mechanism of the anion fragments and dissociation channels of the ion-molecule cluster CF3I·I- in the charge-transfer excited state.