Abstract Future 6th Generation (6G) networks will rely on Terahertz (THz) wireless communication as their main enabler for delivering both ultra-high data speed and minimal delay. THz wireless systems become crucial for upcoming communications by using Unmanned Aerial Vehicles (UAVs) together with Intelligent Reflecting Surfaces (IRS) while improving reliability and efficiency. In UAV-IRS-assisted networks, minimizing mission completion time and energy consumption is critical. However, achieving rapid mission execution often requires UAVs to operate at higher speeds, increasing energy usage and creating a trade-off that demands optimization. This paper addresses the challenge of optimizing UAV-IRS trajectories in THz networks to reduce mission time while adhering to energy constraints. Given the non-convex and NP-hard nature of the problem, traditional optimization methods are insufficient. To tackle this, we propose a Multi-Agent Deep Reinforcement Learning (MADRL) algorithm, which provides an efficient, low-complexity solution for trajectory optimization. MADRL dynamically adapts UAV-IRS paths, balancing mission efficiency and energy savings. Simulation results demonstrate that the proposed MADRL-based approach outperforms existing benchmarks, achieving shorter mission times and near-optimal energy consumption across varying scenarios. By leveraging cooperative learning, the algorithm effectively handles complex environments with multiple users and IRS elements. This work highlights the potential of MADRL for UAV-IRS trajectory optimization, offering a scalable solution for energy-efficient and high-performance THz communication systems.