The asphalt mixture splitting test is one of the most important methods for measuring asphalt’s tensile properties. To characterize the limitations of the traditional splitting test and the influence of the specimen size and loading conditions on the accuracy of the test, the factors affecting the strength of the splitting test were analyzed to reveal the splitting failure state and establish a unified representation model between the splitting and direct tensile tests. Initially, the moment of specimen cracking was taken as a key indicator, combined with image processing technology, to establish a set of criteria to judge the splitting test. Subsequently, standardized splitting tests were conducted and compared to tests of different specimen sizes and loading methods. Based on the octahedral strength theory, the stress points before and after the improved test were compared to the existing failure criteria. Direct tensile and splitting tests were conducted at different rates, and a unified strength–rate function model was established, realizing the unified representation of direct tensile and splitting tests. The research results indicate that the standardized splitting test is prone to the phenomenon wherein the specimen end face cracks before the center, affecting the accuracy of the test and potentially leading to redundant material strength evaluations. Using a loading method with a “35 mm specimen thickness” and a “0.3 mm rubber gasket + 12.7 mm arc-shaped batten” can essentially achieve the test hypothesis of “cracking at the center first”, resulting in less discrete outcomes and closer alignment to the three-dimensional stress failure state. The tensile and splitting strengths are both power function relationships with the rate as the independent variable, establishing a unified function model of the tensile and failure strengths. The research provides a more reliable testing method and calculation model for asphalt pavement structure design, and it also provides an effective basis for the improvement of splitting tests on materials such as concrete and rock.