Messenger RNA (mRNA) vaccines and therapeutics have received intense interest due to their rapid development potential and broad therapeutic applications. However, traditional batch-based manufacturing of these therapeutics faces scalability and consistency challenges. In this work, we present a novel digital twin software specifically tailored for end-to-end continuous mRNA production. The software integrates all key unit operations - In Vitro Transcription (IVT), Tangential Flow Filtration (TFF), Continuous Chromatography (CCTC), Lipid Nanoparticle (LNP) formulation, and Freeze-Drying - within a modular, plug-and-play architecture. We have developed a user-friendly graphical interface that enables process engineers to add, remove, and rearrange modules without coding, while each operation is underpinned by mechanistic models. A built-in database system stores the inputs and outputs of each run, facilitating result retrieval and comparisons. Through an illustrative example involving a representative mRNA production scenario, we demonstrate the seamless simulation of all five operations in silico, generating time series and 3D plots that reveal both process behavior and final product characteristics. Additionally, we used Morris-based global sensitivity analysis for each unit to reveal critical input factors and guide process optimization and model validation. Hence, the software can be used to accelerate process optimization, promotes Quality-by-Design (QbD) principles, and provides a platform for future closed-loop control and operator training. This work supports fully integrated, data-driven continuous manufacturing for mRNA therapeutics, with the potential to enhance scalability, reliability, and responsiveness in the face of global healthcare demands.