Context. Solar filament eruptions usually appear to occur in association with the sudden explosive release of magnetic energy accumulated in long-lived arched magnetic structures. The released energy occasionally drives fast-filament eruptions that can be the source regions of coronal mass ejections. A quantitative analysis of high-speed filament eruptions is thus essential to help elucidate the formation and early acceleration of coronal mass ejections. Aims. The goal of this paper is to investigate the dynamic processes of a fast-filament eruption by using unprecedented high-resolution full-disk Hα imaging spectroscopy observations. Methods. The whole process of the eruption was captured in a wide spectral window of the Hα line (±9.0 Å), which allowed for the detection of highly Doppler-shifted plasma. By applying the “cloud model” and obtaining two-dimensional optical thickness spectra, we derived the Doppler velocity; the true eruption profiles (height, velocity, and acceleration); and the trajectory of the filament eruption in 3D space. Results. The Doppler velocity maps show that the filament was predominantly blueshifted. During the main and final process of the eruption, strongly blueshifted materials manifest, traveling with velocities exceeding 250 km s−1. The spectral analysis further revealed that the erupting filament is made of multiple components, some of which were Doppler-shifted approximately to −300 km s−1. We found that the filament eruption attains a maximum true velocity and acceleration of about 600 km s−1 and 2.5 km s−2, respectively, and its propagation direction deviates from the radial direction. On the other hand, downflows manifested as redshifted plasma close to the footpoints of the erupting filament move with velocities of 45–125 km s−1. We interpret these redshifted signatures as draining material and therefore as mass loss of the filament, which has implications for the dynamic and the acceleration process of the eruption. Furthermore, we have estimated the total mass of the Hα filament, resulting in ∼5.4 × 1015 g.