The systems responsible for mooring floating structures possess a pivotal function in ensuring safety. During harsh marine conditions, mooring systems can be susceptible to failure due to two key factors: mooring line snap tension and out-of-plane loading of the anchor. However, in contemporary mooring designs, these two factors do not receive sufficient contemplation. This paper recommends a safety design strategy for mooring system, which considers both the mooring line snap tension and the out-of-plane loading of the anchor. The analysis of partial mooring line breakage during extreme marine conditions is conducted to elicit insights into the characteristics of floating platform movement, variations in mooring line tension, and the implications of out-of-plane loading on the mooring anchor post breakage. The evolution process of the safety factor is deduced accordingly. The findings reveal that the tensions of adjacent lines experience an abrupt surge when a line is broken, leaving behind the possibility of progressive failure. Due to the vast drift of the floating platform, the adjacent anchors are also troubled by out-of-plane loadings, which dramatically reduce the anchor capacity. This indicates the coupling effect of the mooring line snap tension and the out-of-plane loading as the primary source of failure of the remaining mooring system. The paper emphasizes the significance of factoring in mooring line snap tension and anchor out-of-plane loading capacity verification in anchor design.