False data injection attacks (FDIAs) on smart power grids' measurement data present a threat to system stability. When malicious entities launch cyberattacks to manipulate the measurement data, different grid components will be affected, which leads to failures. For effective attack mitigation, two tasks are required: determining the status of the system (normal operation/under attack) and localizing the attacked bus/power substation. Existing mitigation techniques carry out these tasks separately and offer limited detection performance. In this paper, we propose a multi-task learning-based approach that performs both tasks simultaneously using a graph neural network (GNN) with stacked convolutional Chebyshev graph layers. Our results show that the proposed model presents superior system status identification and attack localization abilities with detection rates of 98.5 - 100% and 99 - 100%, respectively, presenting improvements of 5 - 30% compared to benchmarks.