The dynamics of fast laser-induced vacuum discharge, with a rather small value of amplitude of current (≤ 10 kA), as well as the voltage and energy of the capacitor bank (≤ 20 kV and 20 J, respectively), have been investigated. It has been experimentally demonstrated that the initiations conditions determined by the energy and duration of the laser radiation, fundamentally determine the dynamics of the discharge. Two types of space and time separated plasma instabilities are revealed. It was found that the first of instabilities occurs at the initial stage of the discharge and is caused by a pinch structure, which takes place in front of a cathode jet extending in vacuum. The second type of instabilities arises at the top or recession of the current and is accompanied by the generation of hard (energy ≥100 keV) bremsstrahlung X-ray radiation from the anode area. The excess energy of the hard components of radiation over the potential of the current source is associated with the effects of plasma-erosive breaking.