The increasing adoption of rooftop photovoltaic (PV) power generation systems in residential areas necessitates accurate monitoring and disaggregation of behind-the-meter (BTM) load and PV power. Despite recent advancements, existing BTM disaggregation approaches suffer from three major drawbacks: neglecting task-relevant spatiotemporal features, overfitting, and lack of a sparse neural architecture which leads to high sample complexity. This paper addresses them by introducing a deep sparse attention graph recurrent framework. This framework conceptualizes a set of neighboring residential units as a graph where the nodes are the net load values of the units and the edges show the mutual information (MI) of these measurements. We develop an Attention Gated Recurrent Unit (AGRU) to capture enhanced temporal characteristics of the net load. We employ a novel low-rank Dictionary Learning (DL) method to discern spatiotemporal features of these measurements and further utilize a Rectified Linear Unit (ReLU) neural network that incorporates an MI-based dropout to provide a sparse model for the estimation of the BTM load and PV. Experimental results validate the effectiveness of our proposed model, exhibiting superior performance on the Ausgrid dataset in BTM load and PV power estimation compared to state-of-the-art methods.