Federated learning is a distributed learning paradigm that facilitates the collaborative training of a global model across multiple clients while preserving the privacy of local datasets. To address inherent challenges related to data heterogeneity and satisfy personalized needs, a new direction within FL, known as personalized Federated Learning (pFL), has gradually evolved. Extensive attention has been directed toward developing novel frameworks and methods to enhance the performance of pFL. Regrettably, the aspect of security in pFL has been largely overlooked. Our objective is to fill this gap. Similar to FL, pFL is susceptible to backdoor attacks. However, existing backdoor defense strategies are primarily tailored to general FL frameworks, and pFL lacks robustness against backdoor attacks. We propose a novel, backdoor-robust pFL framework named BDPFL to address these challenges. First, BDPFL introduces layer-wise mutual distillation that enables clients to learn their personalized local models while mitigating potential backdoors. Then, BDPFL employs explanation heatmap to learn high-quality intermediate representations and enhance the effect of eliminating deeper and more entrenched backdoors. Moreover, we perform empirical evaluations of BDPFL's performance on three datasets and compare BDPFL with four backdoor defense methods. The experiments demonstrate that BDPFL outperforms baseline methods and is effective under various settings.