Rock blasting technology plays an important role in the construction of infrastructural projects such as tunnel excavation and mining. The plasma rock breaking technology is characterized with no pollution, no flying stones or harmful gases in the blasting process, easy operation and high efficiency, and is the most effective and feasible method to replace the explosive. In this paper, the rock breaking mechanism of plasma generated by underwater wire explosion is studied. The process of copper wire melting during high-voltage pulse discharge is analyzed. The resistance model of copper wires changes at various stages is established. Numerical simulation analysis is performed of the current of the discharge circuit at different stages with MATLAB and compared with the experimental current waveform. The study finds that the shorter the rising edge time of the current waveform, the better the pulse discharge effect. During the process of generating a plasma by a copper wire, the plasma channel has certain electrical resistance. The experimental results are basically consistent with the model numerical calculation results.