Direct air capture (DAC), as a complementary strategy to carbon capture and storage (CCS), offers a scalable and sustainable pathway to remove CO₂ directly from the ambient air. This study presents a detailed evaluation of the amine-functionalised metal-organic framework (MOF) sorbent, mmen-Mg₂(dobpdc), for DAC using a temperature–vacuum swing adsorption (TVSA) process. While this sorbent has demonstrated promising performance in point-source CO₂ capture, this is the first dynamic simulation-based study to rigorously assess its effectiveness for low-concentration atmospheric CO₂ removal. A transient one-dimensional TVSA model was developed in Aspen Adsorption and validated against experimental breakthrough data to ensure accuracy in capturing both the sharp and gradual adsorption kinetics. To enhance process efficiency and sustainability, this work provides a comprehensive parametric analysis of key operational factors, including air flow rate, temperature, adsorption/desorption durations, vacuum pressure, and heat exchanger temperature, on process performance, including CO₂ purity, recovery, productivity, and specific energy consumption. Under optimal conditions for this sorbent (vacuum pressure lower than 0.15 bar and feed temperature below 15 °C), the TVSA process achieved ~98% CO₂ purity, recovery over 70%, and specific energy consumption of about 3.5 MJ/KgCO₂. These findings demonstrate that mmen-Mg₂(dobpdc) can achieve performance comparable to benchmark DAC sorbents in terms of CO₂ purity and recovery, underscoring its potential for scalable DAC applications. This work advances the development of energy-efficient carbon removal technologies and highlights the value of step-shape isotherm adsorbents in supporting global carbon-neutrality goals.