Dwarf galaxy streams encode rich information that is essential to understand early galaxy formation and nucleosynthesis channels. Due to various timescales of star formation history in their progenitors, they serve as "snapshots" that record different stages of galactic chemical evolution. This study focuses on the Cetus stream stripped from a low-mass dwarf galaxy. We aim to uncover its chemical evolution history as well as different channels of its elements production from the detailed elemental abundances. We provide a comprehensive analysis of the chemical composition of 22 member stars based on their high-resolution spectra. We derive abundances for up to 28 chemical species from C to Dy and, for 20 of them, we account for the departures from the local thermodynamic equilibrium (non-LTE effects). We confirm that the Cetus stream has a mean metallicity [Fe/H]=-2.11+/-0.21. All observed Cetus stars are alpha enhanced with [alpha/Fe]~0.3. The absence of the alpha-"knee" implies the star formation stopped before iron production in type Ia supernovae (SNe Ia) became substantial. Neutron capture element abundances suggest that both r-process and main s-process contributed to their origin. The decrease in [Eu/Ba] from a typical r-process value [Eu/Ba]=0.7 to 0.3 with increasing [Ba/H] indicates a distinct contribution of the r- and s-processes in chemical composition of different Cetus stars. For barium, the r-process contribution varies from 100% to 20% in different sample stars, with an average value of 50%. Our abundance analysis indicates that the star formation in the Cetus progenitor ceased after the onset of the main s-process in low-intermediate mass asymptotic giant branch stars but before SNe Ia played an important role. A distinct evolution scenario is revealed by comparing the abundances in the Ursa Minor dwarf spheroidal galaxy, showing the diversity and uniqueness in the chemical evolution of low-mass dwarf galaxies.