Context. Ubiquitous small-scale vortices have recently been found in the lower atmosphere of the quiet Sun in state-of-the-art solar observations and in numerical simulations. Aims. We investigate the characteristics and temporal evolution of a granular-scale vortex and its associated upflows through the photosphere and chromosphere of a quiet Sun internetwork region. Methods. We analyzed high spatial and temporal resolution ground- and spaced-based observations of a quiet Sun region. The observations consist of high-cadence time series of wideband and narrowband images of both Hα 6563 Å and Ca II 8542 Å lines obtained with the CRisp Imaging SpectroPolarimeter (CRISP) instrument at the Swedish 1-m Solar Telescope (SST), as well as ultraviolet imaging and spectral data simultaneously obtained by the Interface Region Imaging Spectrograph (IRIS). Results. A small-scale vortex is observed for the first time simultaneously in Hα, Ca II 8542 Å, and Mg II k lines. During the evolution of the vortex, Hα narrowband images at −0.77 Å and Ca II 8542 Å narrowband images at −0.5 Å, and their corresponding Doppler signal maps, clearly show consecutive high-speed upflow events in the vortex region. These high-speed upflows with a size of 0.5–1 Mm appear in the shape of spiral arms and exhibit two distinctive apparent motions in the plane of sky for a few minutes: (1) a swirling motion with an average speed of 13 km s-1 and (2) an expanding motion at a rate of 4–6 km s-1. Furthermore, the spectral analysis of Mg II k and Mg II subordinate lines in the vortex region indicates an upward velocity of up to ~8 km s-1 along with a higher temperature compared to the nearby quiet Sun chromosphere. Conclusions. The consecutive small-scale vortex events can heat the upper chromosphere by driving continuous high-speed upflows through the lower atmosphere.