We develop a dynamic spin-lattice-electron model for simulating the time-dependent evolution of coupled spin, atomic, and electronic degrees of freedom in a magnetic material. Using the model, we relate the dissipative parameters entering the Langevin equations for the lattice and spin degrees of freedom to the heat transfer coefficients of a phenomenological spin-lattice-electron three-temperature model.We apply spin-lattice-electron dynamics simulations to the interpretation of experiments on laser-induced demagnetization of iron thin films, and estimate the rates of heat transfer between the spins and electrons, and between atoms and electrons. To model the dynamics of energy dissipation in a magnetic material undergoing plastic deformation, we develop an algorithm that separates the local collective modes of motion of atoms from their random thermal motion. Using this approach, we simulate the propagation of compressive shock waves through magnetic iron. We also explore the microscopic dynamics of dissipative coupling between the spin and lattice subsystems, and show that the rate of spin-lattice heat transfer is proportional to the integral of the four-spin time-dependent correlation function.