Salty sweat secretions in the epidermis change the skin's electrical activity resulting in the measured skin conductance signal. While the relatively fast variation of skin conductance (i.e. phasic component) reflects sympathetic nervous system activity, the slow variation (i. e. tonic component) is related to thermoregulation and general arousal. To better understand the neural information encoded in a skin conductance signal, it is necessary to decompose it into its constituent components. We model the fast variations using a second order differential equation incorporating a sparse impulsive input to the model. Furthermore, we model the tonic component with several cubic basis spline functions. Finally, we develop a block coordinate descent approach for skin conductance signal decomposition by employing generalized-cross-validation for balancing between smoothness of the tonic component, the sparsity of the neural stimuli, and residual error. We analyze experimental and simulated data to validate the performance of the proposed approach. We successfully illustrate its ability to recover the neural stimuli, the underlying physiological system parameters, and both tonic and phasic components. In summary, we develop a novel approach for decomposition of phasic and tonic components of skin conductance signal using a generalized-cross-validation-based block coordinate descent approach. Recovering the underlying neural stimuli and the tonic component accurately could potentially improve cognitive-stress-related arousal states estimation for better stress regulation in mental health disorders.