We modify the coupling method established in Shirikyan (Exponential mixing for randomly forced partial differential equations: method of coupling, Springer, New York, 2008) and Shirikyan (J Math Fluid Mech 6(2):169-193, 2004) and develop a technique to prove the exponential mixing of a 2D stochastic system forced by degenerate L,vy noises. In particular, these L,vy noises include alpha-stable noises (0 < alpha < 2). Thanks to the stimulating discussion (Nersesyan in Private communication 2011), this technique is promising to study the exponential mixing problem of SPDEs driven by degenerate symmetric alpha-stable noises.