Self-supervised learning (SSL) is increasingly attractive for pre-training encoders without requiring labeled data. Downstream tasks built on top of those pre-trained encoders can achieve nearly state-of-the-art performance. The pre-trained encoders by SSL, however, are vulnerable to backdoor attacks as demonstrated by existing studies. Numerous backdoor mitigation techniques are designed for downstream task models. However, their effectiveness is impaired and limited when adapted to pre-trained encoders, due to the lack of label information when pre-training. To address backdoor attacks against pre-trained encoders, in this paper, we innovatively propose a mutual information guided backdoor mitigation technique, named MIMIC. MIMIC treats the potentially backdoored encoder as the teacher net and employs knowledge distillation to distill a clean student encoder from the teacher net. Different from existing knowledge distillation approaches, MIMIC initializes the student with random weights, inheriting no backdoors from teacher nets. Then MIMIC leverages mutual information between each layer and extracted features to locate where benign knowledge lies in the teacher net, with which distillation is deployed to clone clean features from teacher to student. We craft the distillation loss with two aspects, including clone loss and attention loss, aiming to mitigate backdoors and maintain encoder performance at the same time. Our evaluation conducted on two backdoor attacks in SSL demonstrates that MIMIC can significantly reduce the attack success rate by only utilizing <5% of clean data, surpassing seven state-of-the-art backdoor mitigation techniques.