In recent years, quantum-dot (QD) semiconductor lasers attract significant interest in many practical applications due to their advantages such as high-power pulse generation because to the high gain efficiency. In this work, the pulse shape of an electrically pumped QD-laser under high current is analyzed. We find that the slow rise time of the pulsed pump may significantly affect the high intensity output pulse. It results in sharp power dropouts and deformation of the pulse profile. We address the effect to dynamical change of the phase-amplitude coupling in the proximity of the excited state (ES) threshold. Under 30ns pulse pumping, the output pulse shape strongly depends on pumping amplitude. At lower currents, which correspond to lasing in the ground state (GS), the pulse shape mimics that of the pump pulse. However, at higher currents the pulse shape becomes progressively unstable. The instability is greatest when in proximity to the secondary threshold which corresponds to the beginning of the ES lasing. After the slow rise stage, the output power sharply drops out. It is followed by a long-time power-off stage and large-scale amplitude fluctuations. We explain these observations by the dynamical change of the alpha-factor in the QD-laser and reveal the role of the slowly rising pumping processes in the pulse shaping and power dropouts at higher currents. The modeling is in very good agreement with the experimental observations.