Knowledge transfer between multi-omic single-cell data aims to effectively transfer cell types from scRNA-seq data to unannotated scATAC-seq data. Several approaches aim to reduce the heterogeneity of multi-omic data while maintaining the discriminability of cell types with extensive annotated data. However, in reality, the cost of collecting both a large amount of labeled scRNA-seq data and scATAC-seq data is expensive. Therefore, this paper explores a practical yet underexplored problem of knowledge transfer across multi-omic single-cell data under cell type scarcity. To address this problem, we propose a semi-supervised knowledge transfer framework named Dual label scArcity elimiNation with Cross-omic multi-samplE Mixup (DANCE). To overcome the label scarcity in scRNA-seq data, we generate pseudo-labels based on optimal transport and merge them into the labeled scRNA-seq data. Moreover, we adopt a divide-and-conquer strategy which divides the scATAC-seq data into source-like and target-specific data. For source-like samples, we employ consistency regularization with random perturbations while for target-specific samples, we select a few candidate labels and progressively eliminate incorrect cell types from the label set for additional supervision. Next, we generate virtual scRNA-seq samples with multi-sample Mixup based on the class-wise similarity to reduce cell heterogeneity. Extensive experiments on many benchmark datasets suggest the superiority of our DANCE over a series of state-of-the-art methods.