Can the mutual information of a "cell" be negative?
By the simple transformation $p(x_0, y) = p(x_0) p(y | x_0)$ your expression merely becomes $p(x_0) KL(p (y|x), p(y))$, where $KL(p,q)$ is the Kullback-Leibler divergence, and is always positive. therefore, your expression is always positive.