The fate of entanglement of spins for two heavy constituents of a bound state moving in a strong laser field is analyzed within the semiclassical approach. The bound state motion as a whole is considered classically beyond the dipole approximation and taking into account the magnetic field effect by using the exact solution to the Newton equation. At the same time the evolution of constituent spins under the laser influence is studied quantum mechanically. The spin density matrix is determined as solution to the von Neumann equation with the effective Hamiltonian, describing spin-laser interaction along the bound state classical trajectory. Based on the solution, the dynamics of concurrence of spins is calculated for the maximally entangled Werner states as well as for an initially uncorrelated state.