Unmanned Aerial Vehicles (UAVs), also known as drones, have gained popularity in various fields such as agriculture, emergency response, and search and rescue operations. UAV networks are susceptible to several security threats, such as wormhole, jamming, spoofing, and false data injection. Time Delay Attack (TDA) is a unique attack in which malicious UAVs intentionally delay packet forwarding, posing significant threats, especially in time-sensitive applications. It is challenging to distinguish malicious delay from benign network delay due to the dynamic nature of UAV networks, intermittent wireless connectivity, or the Store-Carry-Forward (SCF) mechanism during multi-hop communication. Some existing works propose machine learning-based centralized approaches to detect TDA, which are computationally intensive and have large message overheads. This paper proposes a novel approach DATAMUt, where the temporal dynamics of the network are represented by a weighted time-window graph (TWiG), and then two deterministic polynomial-time algorithms are presented to detect TDA when UAVs have global and local network knowledge. Simulation studies show that the proposed algorithms have reduced message overhead by a factor of five and twelve in global and local knowledge, respectively, compared to existing approaches. Additionally, our approaches achieve approximately 860 and 1050 times less execution time in global and local knowledge, respectively, outperforming the existing methods.