This work describes the traditional wet and green synthetic approaches, structural features, and extensive bioactivity study for a new coordination polymer [Ag(μ-PTA)(Df)(H2O)]n·3nH2O (1) that bears a silver(I) center, a 1,3,5-triaza-phosphaadamantane (PTA) linker, and a nonsteroidal anti-inflammatory drug, diclofenac (Df-). Compared to cisplatin, compound 1 exhibits both anti-inflammatory properties and very remarkable cytotoxicity toward various cancer cell lines with a high value of selectivity index. Additionally, the 3D model representing human pancreas/duct carcinoma (PANC-1) and human lung adenocarcinoma (A549) was designed and applied as a clear proof of the remarkable therapeutic potential of 1. The obtained experimental data indicate that 1 induces an apoptotic pathway via reactive oxygen species generation, targeting mitochondria due to their membrane depolarization. This study broadens a group of bioactive metal-organic networks and highlights the significant potential of such compounds in developing advanced therapeutic solutions.