In this paper, the stability and stabilization issues are investigated for a class of discrete-time switched piecewise affine systems with modal average dwell time switching. Both the autonomous (state-partition-dependent) switching and the controlled (modal average dwell time) switching appear concurrently in the studied system. At first, the exponential stability criterion is derived using the proposed piecewise quadratic Lyapunov function approach. Then the state feedback controller in the piecewise affine form is designed to achieve stabilization for the resulting closed-loop switched piecewise affine system. In the end, the effectiveness and accuracy of the theoretical findings are testified via a numerical example.