Herein we employed high-resolution spectroscopic techniques in combination with periodic ab initio density functional theory (DFT) calculations to establish the different polarization processes for a porous copper-based MOF, termed HKUST-1. We used alternating current measurements to determine its dielectric response between 4 Hz and 1.5 MHz where orientational polarization is predominant, while synchrotron infrared (IR) reflectance was used to probe the far-IR, mid-IR, and near-IR dielectric response across the 1.2 THz to 150 THz range (ca. 40 - 5000 cm^-1) where vibrational and optical polarizations are principal contributors to its dielectric permittivity. We demonstrate the role of pressure on the evolution of broadband dielectric response, where THz vibrations reveal distinct blue and red shifts of phonon modes from structural deformation of the copper paddle-wheel and the organic linker, respectively. We also investigated the effect of temperature on dielectric constants in the MHz region pertinent to microelectronics, to study temperature-dependent dielectric losses via dissipation in an alternating electric field. The DFT calculations offer insights into the physical mechanisms responsible for dielectric transitions observed in the experiments and enable us to explain the frequency shifts phenomenon detected under pressure. Together, the experiments and theory have enabled us to glimpse into the complex dielectric response and mechanisms underpinning a prototypical MOF subject to pressure, temperature, and vast frequencies.