Based on the Lagrangian description, a single temperature magneto-hydrodynamics model of underwater electrical wire explosion is established, and a high-order mixed finite element method is used to solve this model. For the Lagrangian compressible fluid equations, velocity is discretized using the continuous high-order basis function in the H1 space, and internal energy is discretized using a L2 piecewise discontinuous high-order basis function for the precise capture of the material interface. A tensor artificial viscosity is introduced to suppress the numerical oscillation. Only the azimuthal magnetic flux density is contained in the magnetic diffusion equation, which is simplified to a scalar equation, and is discretized using continuous basis function. Joule heating and Lorenz force are introduced to couple hydrodynamics equations with magnetic field. Numerical results show that the magneto-diffusion solver can solve a multi-material magnetic diffusion problem, and the hydrodynamics solver can track the material interface and shock wave. Underwater electrical wire explosion is simulated based on the magneto-hydrodynamics solver coupled with RLC circuit, including phase transition, shock wave and different discharge modes.