Most available tests of asphalt mixture performance against moisture damage or the effect of additives examined the asphalt mixture’s overall performance. Considering the different mechanisms of moisture damage, studying antistripping additives’ effect on failure mechanisms might provide a better view of the asphalt mixture’s performance against moisture. Accordingly, herein, the effects of various antistripping additives, including a liquid antistripping additive (dodecylamine) and a nano-magnesium hydroxide additive, each at two bitumen weight percentages, with two types of aggregates with different mineralogical properties and a PG 64-16 bitumen on moisture damage mechanism were investigated. The cohesion and adhesion mechanisms of moisture damage were examined using the pull off test, and the asphalt mixture’s overall performance was assessed using the indirect tensile strength (ITS) test in multiple dry and wet conditions (1, 2, and 3 freeze-thaw cycles) according to the modified Lottman test. The results revealed that the use of 0.4% dodecylamine and 1% nano-magnesium hydroxide in the mixtures made with lime aggregates increases the tensile strength ratio (TSR) from 62.67% to 85.4% and 84.8%, respectively. In mixtures made with granite aggregates, TSR increased from 54.45% to 72.49% and 71.35%, respectively. The failure mechanisms’ assessment showed that the use of 1% nano-magnesium hydroxide in mixtures made with granite aggregate elevated the pull off in the adhesion failure mechanism by 80%, and the pull off increased by 70% in the cohesion failure mechanism. Moreover, the pull off increased by 63% for limestone mixtures in the cohesion failure mechanism and by 56% in the adhesion failure mechanism. The dodecylamine additive with the highest pull off and ITS ratio in all freeze-thaw cycles was more suitable than nano-magnesium hydroxide to promote the asphalt mixtures’ overall performance against moisture. The statistical analysis also indicated the significant effect of dodecylamine and nano-magnesium hydroxide additives on asphalt mixtures’ moisture sensitivity reduction at a 95% confidence level. The findings show that some additives have a stronger effect on adhesion strength and some effect on cohesion strength, but the additive that better improves the overall asphalt mix performance depends on mix design characteristics and aggregate and bitumen type.