Mangrove-forest classification by using deep learning algorithms has attracted increasing attention but remains challenging. The current studies on the transfer classification of mangrove communities between different regions and different sensors are especially still unclear. To fill the research gap, this study developed a new deep-learning algorithm (encoder–decoder with mixed depth-wise convolution and cascade upsampling, MCCUNet) by modifying the encoder and decoder sections of the DeepLabV3+ algorithm and presented three transfer-learning strategies, namely frozen transfer learning (F-TL), fine-tuned transfer learning (Ft-TL), and sensor-and-phase transfer learning (SaP-TL), to classify mangrove communities by using the MCCUNet algorithm and high-resolution UAV multispectral images. This study combined the deep-learning algorithms with recursive feature elimination and principal component analysis (RFE–PCA), using a high-dimensional dataset to map and classify mangrove communities, and evaluated their classification performance. The results of this study showed the following: (1) The MCCUNet algorithm outperformed the original DeepLabV3+ algorithm for classifying mangrove communities, achieving the highest overall classification accuracy (OA), i.e., 97.24%, in all scenarios. (2) The RFE–PCA dimension reduction improved the classification performance of deep-learning algorithms. The OA of mangrove species from using the MCCUNet algorithm was improved by 7.27% after adding dimension-reduced texture features and vegetation indices. (3) The Ft-TL strategy enabled the algorithm to achieve better classification accuracy and stability than the F-TL strategy. The highest improvement in the F1–score of Spartina alterniflora was 19.56%, using the MCCUNet algorithm with the Ft-TL strategy. (4) The SaP-TL strategy produced better transfer-learning classifications of mangrove communities between images of different phases and sensors. The highest improvement in the F1–score of Aegiceras corniculatum was 19.85%, using the MCCUNet algorithm with the SaP-TL strategy. (5) All three transfer-learning strategies achieved high accuracy in classifying mangrove communities, with the mean F1–score of 84.37%~95.25%.