The regulation of the cell division cycle is governed by a complex network of factors that together ensure that growing or proliferating cells maintain a stable genome. Defects in this system can lead to genomic instability that can affect tissue homeostasis and thus compromise human health. Variations in ploidy and cell heterogeneity are observed frequently in human cancers. Here, we examine the consequences of upregulating the cell cycle regulator Cyclin E in the Drosophila melanogaster male accessory gland. The accessory gland is the functional analog of the human prostate. This organ is composed of a postmitotic epithelium that is emerging as a powerful in vivo system for modelling different aspects of tumor initiation and progression. We show that Cyclin E upregulation in this model is sufficient to drive tissue dysplasia. Cyclin E overexpression drives endoreplication and affects DNA integrity, which results in heterogeneous nuclear and cellular composition and variable degrees of DNA damage. We present evidence showing that, despite the presence of genotoxic stress, those cells are resistant to apoptosis and thus defective cells are not eliminated from the tissue. We also show that Cyclin E-expressing cells in the accessory gland display mitochondrial DNA aggregates that colocalize with Cyclin E protein. Together, the findings presented here show that Cyclin E upregulation in postmitotic cells of the accessory gland organ causes cellular defects such as genomic instability and mitochondrial defects, eventually leading to tissue dysplasia. This study highlights novel mechanisms by which Cyclin E might contribute to disease initiation and progression.