We analyze high temporal and spatial resolution time series of spectral scans of the Hα line obtained with the CRisp Imaging SpectroPolarimeter instrument mounted on the Swedish Solar Telescope. The data reveal highly dynamic, dark, short-lived structures known as Rapid Redshifted and Blueshifted Excursions (RREs, RBEs) that are on-disk absorption features observed in the red and blue wings of spectral lines formed in the chromosphere. We study the dynamics of RREs and RBEs by tracking their evolution in space and time, measuring the speed of the apparent motion, line of sight (LOS) Doppler velocity, and transverse velocity of individual structures. A statistical study of their measured properties shows that RREs and RBEs have similar occurrence rates, lifetimes, lengths, and widths. They also display non-periodic, nonlinear transverse motions perpendicular to their axes at speeds of 4–31 km s−1. Furthermore, both types of structures either appear as high speed jets and blobs that are directed outwardly from a magnetic bright point with speeds of 50–150 km s−1, or emerge within a few seconds. A study of the different velocity components suggests that the transverse motions along the LOS of the chromospheric flux tubes are responsible for the formation and appearance of these redshifted/blueshifted structures. The short lifetime and fast disappearance of the RREs/RBEs suggests that, similar to type II spicules, they are rapidly heated to transition region or even coronal temperatures. We speculate that the Kelvin Helmholtz instability triggered by observed transverse motions of these structures may be a viable mechanism for their heating.