Recognition and quantitative analytics of histopathological cells are the golden standard for diagnosing multiple cancers. Despite recent advances in deep learning techniques that have been widely investigated for the automated segmentation of various types of histopathological cells, the heavy dependency on specific histopathological image types with sufficient supervised annotations, as well as the limited access to clinical data in hospitals, still pose significant challenges in the application of computer-aided diagnosis in pathology. In this paper, we focus on the model generalization of cell segmentation towards cross-tissue histopathological images. Remarkably, a novel target-specific finetuning-based self-supervised domain adaptation framework is proposed to transfer the cell segmentation model to unlabeled target datasets, without access to source datasets and annotations. When performed on the target unlabeled histopathological image set, the proposed method only needs to tune very few parameters of the pre-trained model in a self-supervised manner. Considering the morphological properties of pathological cells, we introduce two constraint terms at both local and global levels into this framework to access more reliable predictions. The proposed cross-domain framework is validated on three different types of histopathological tissues, showing promising performance in self-supervised cell segmentation. Additionally, the whole framework can be further applied to clinical tools in pathology without accessing the original training image data. The code and dataset are released at: https://github.com/NeuronXJTU/SFDA-CellSeg.