Morphological segmentation for polysynthetic languages is challenging, because a word may consist of many individual morphemes and training data can be extremely scarce. Since neural sequence-to-sequence (seq2seq) models define the state of the art for morphological segmentation in high-resource settings and for (mostly) European languages, we first show that they also obtain competitive performance for Mexican polysynthetic languages in minimal-resource settings. We then propose two novel multi-task training approaches—one with, one without need for external unlabeled resources—, and two corresponding data augmentation methods, improving over the neural baseline for all languages. Finally, we explore cross-lingual transfer as a third way to fortify our neural model and show that we can train one single multi-lingual model for related languages while maintaining comparable or even improved performance, thus reducing the amount of parameters by close to 75%. We provide our morphological segmentation datasets for Mexicanero, Nahuatl, Wixarika and Yorem Nokki for future research.