This paper presents a method for segmenting iris images obtained from the deceased subjects, by training a deep convolutional neural network (DCNN) designed for the purpose of semantic segmentation. Post-mortem iris recognition has recently emerged as an alternative, or additional, method useful in forensic analysis. At the same time it poses many new challenges from the technological standpoint, one of them being the image segmentation stage, which has proven difficult to be reliably executed by conventional iris recognition methods. Our approach is based on the SegNet architecture, fine-tuned with 1,300 manually segmented post-mortem iris images taken from the Warsaw-BioBase-Post-Mortem-Iris v1.0 database. The experiments presented in this paper show that this data-driven solution is able to learn specific deformations present in post-mortem samples, which are missing from alive irises, and offers a considerable improvement over the state-of-the-art, conventional segmentation algorithm (OSIRIS): the Intersection over Union (IoU) metric was improved from 73.6% (for OSIRIS) to 83% (for DCNN-based presented in this paper) averaged over subject-disjoint, multiple splits of the data into train and test subsets. This paper offers the first known to us method of automatic processing of post-mortem iris images. We offer source codes with the trained DCNN that perform end-to-end segmentation of post-mortem iris images, as described in this paper. Also, we offer binary masks corresponding to manual segmentation of samples from Warsaw-BioBase-Post-Mortem-Iris v1.0 database to facilitate development of alternative methods for post-mortem iris segmentation.