Electroencephalogram (EEG)-based seizure subtype classification enhances clinical diagnosis efficiency. Source-free semi-supervised domain adaptation (SF-SSDA), which transfers a pre-trained model to a new dataset with no source data and limited labeled target data, can be used for privacy-preserving seizure subtype classification. This paper considers two challenges in SF-SSDA for EEG-based seizure subtype classification: 1) How to effectively fuse both raw EEG data and expert knowledge in classifier design? 2) How to align the source and target domain distributions for SF-SSDA? We propose a Knowledge-Data Fusion based SF-SSDA approach, KDF-MutualSHOT, for EEG-based seizure subtype classification. In source model training, KDF uses Jensen-Shannon Divergence to facilitate mutual learning between a feature-driven Decision Tree-based model and a data-driven Transformer-based model. To adapt KDF to a new target dataset, an SF-SSDA algorithm, MutualSHOT, is developed, which features a consistency-based pseudo-label selection strategy. Experiments on the public TUSZ and CHSZ datasets demonstrated that KDF-MutualSHOT outperformed other supervised and source-free domain adaptation approaches in cross-subject seizure subtype classification.