In view of the widely existed two-dimensional friction problems in engineering, an oscillator model which considers the coupling of and direction is established by introducing oblique springs. With the concept of the friction force direction angle being defined to determine the components of the static and kinetic friction force vector, and considering that stick-slip motion may occur when the oscillator is vibrating, a method for analyzing stick-slip motion of a two-dimensional coupled dry friction oscillator is proposed, and complex stick-slip transition boundaries of the two-dimensional coupled dry friction oscillator are given. Based on an exponential-type dynamic friction model, numerical simulation is carried out for stick-slip motion of the two-dimensional coupled dry friction oscillator, with the simulation results and the law of the system solution changing with excitation frequency and phase angle under three different working conditions at x direction and y direction, namely the same excitation frequency and phase angle, the same excitation frequency and different phase angle, and different excitation frequency and phase angle, are provided. Numerical results indicate that transition of stick-slip state may occur in the motion of the two-dimensional coupled dry friction oscillator; in comparison with the first two conditions, when frequencies and phase angle of and direction of the excitation are not equal, trajectory of the mass is a more complicated plane curve, the system can have multiple stick-slip transitions in one cycle at the same time; with the same frequency of and direction, the response of the oscillator has no fractional frequencies and is periodic by altering the frequency and phase angle. The proposed method can provide reference for further study of dynamics and motion stability of a two-dimensional coupled dry friction oscillator.