Strength is an important parameter for the design of asphalt pavement materials and structures. To study the influence of various factors on the three-dimensional strength of asphalt mixtures, three aggregate gradations (dense-graded bituminous mixture AC-13, stone mastic asphalt SMA-13 and bituminous stabilization aggregate paving mixture OGFC-13) and two binders (SBS modified bitumen and 70# base bitumen) were used to prepare the asphalt mixture specimens. Among them, SBS+SMA-13 asphalt mixture has the best performance. On this basis, the uniaxial compressive test, uniaxial tensile test and confining triaxial test were conducted on the SBS+SMA-13 asphalt mixture under six oil-stone ratios conditions (5.5%, 5.7%, 5.9%, 6.1%, 6.3%, and 6.5%), six temperatures conditions (5 °C, 10 °C, 15 °C, 20 °C, 25 °C, and 30 °C), and five loading rates conditions (1 mm/min, 2 mm/min, 3 mm/min, 4 mm/min, and 5 mm/min). In addition, a unified three-dimensional strength calculation model considering the influence of temperature, loading rate, and oil-stone ratio was proposed, and the change law of the three-dimensional strength with these above factors was revealed. Furthermore, two sets of three-factor three-level orthogonal tests were carried out on the SMA-13 asphalt mixture. The sensitivity analysis and strength regulation research between three-dimensional strength and each factor were carried out. The results show that the type of asphalt has the greatest influence on the strength of the mixture, the temperature has the second most influence, the loading rate has less influence, and the oil-stone ratio has the least influence. The strength regulations proposed to improve the strength of the asphalt mixture include the use of modified asphalt, high-temperature stability high-quality asphalt, and the lower oil-stone ratio than the Marshall optimal oil-stone ratio. The strength control measures proposed from the perspective of the three-dimensional stress state, the joint failure of each stress components and real stress states are taken into consideration.