Context. Protostellar jets and outflows are an important agent of star formation as they carry away a fraction of momentum and energy, which is needed for gravitational collapse and protostellar mass accretion to occur. Aims. Our goal is to provide constraints on the dynamics of the inner protostellar environment from the study of the outflow-jet propagation away from the launch region. Methods. We have used the axisymmetric chemo-hydrodynamical code W ALKIMYA -2D to numerically model and reproduce the physical and CO emission properties of the jet-driven outflow from the intermediate-mass protostar CepE-mm, which was observed at ~800 au resolution in the CO J = 2−1 line with the IRAM interferometer. Our simulations take into account the observational constraints available on the physical structure of the protostellar envelope. Results. W ALKIMYA -2D successfully reproduces the main qualitative and quantitative features of the Cep E outflow and the jet kinematics, naturally accounting for their time variability. Signatures of internal shocks are detected as knots along the jet. In the early times of the ejection process, the young emitted knots interact with the dense circumstellar envelope through high-velocity, dissociative shocks, which strongly decrease the CO gas abundance in the jet. As time proceeds, the knots propagate more smoothly through the envelope and dissociative shocks disappear after ~10 3 yr. The distribution of CO abundance along the jet shows that the latter bears memory of the early dissociative phase in the course of its propagation. Analysis of the velocity field shows that the jet material mainly consists of gas entrained from the circumstellar envelope and accelerated away from the protostar at 700 au scale. As a result, the overall jet mass-loss rate appears higher than the actual mass-ejection rate by a factor ~3. Conclusions. Numerical modeling of the Cep E jet-driven outflow and comparison with the CO observations have allowed us to peer into the outflow formation mechanism with unprecedented detail and to retrieve the history of the mass-loss events that have shaped the outflow.