Both limited annotation and domain shift are prevalent challenges in medical image segmentation. Traditional semi-supervised segmentation and unsupervised domain adaptation methods address one of these issues separately. However, the coexistence of limited annotation and domain shift is quite common, which motivates us to introduce a novel and challenging scenario: \textbf{Mi}xed \textbf{D}omain \textbf{S}emi-supervised medical image \textbf{S}egmentation (MiDSS). In this scenario, we handle data from multiple medical centers, with limited annotations available for a single domain and a large amount of unlabeled data from multiple domains. We found that the key to solving the problem lies in how to generate reliable pseudo labels for the unlabeled data in the presence of domain shift with labeled data. To tackle this issue, we employ Unified Copy-Paste (UCP) between images to construct intermediate domains, facilitating the knowledge transfer from the domain of labeled data to the domains of unlabeled data. To fully utilize the information within the intermediate domain, we propose a symmetric Guidance training strategy (SymGD), which additionally offers direct guidance to unlabeled data by merging pseudo labels from intermediate samples. Subsequently, we introduce a Training Process aware Random Amplitude MixUp (TP-RAM) to progressively incorporate style-transition components into intermediate samples. Compared with existing state-of-the-art approaches, our method achieves a notable 13.57\% improvement in Dice score on Prostate dataset, as demonstrated on three public datasets. Our code is available in the supplementary material.