In the environmental modeling field, the exploratory analysis of responses often exhibits spatial correlation as well as some non-Gaussian attributes such as skewness and/or heavy-tailedness. Consequently, we propose a general spatial model based on scale-shape mixtures of the multivariate skew-normal distribution. Intuitively, it incorporates distinct random effects to account for the spatial dependencies not explained by a simple Gaussian random field model. Importantly, the proposed model is capable of generating a wide range of skewness and kurtosis levels. Meanwhile, we demonstrate that the skewness mixing can induce asymmetric tail dependence at sub-asymptotic and/or asymptotic levels.