To obtain a crumb rubber asphalt mixture with excellent performance, this study combined trans-polyoctenamer rubber (TOR), crumb rubber, and other additives to establish a new type of crumb rubber (CRT). The objective of this study was to design and evaluate the road performance of the new type of crumb rubber asphalt mixture (CRTAM) with a skeleton dense texture through a dry process. First, the skeleton intrusion compact volume method was used to optimize the grading of coarse and fine aggregates, and the design of the CRTAM gradation was carried out through the same and unequal volume replacement grading method. Then, three types of road performance were analyzed: high-temperature stability, low-temperature crack resistance, and water stability. The results showed that 2% and 2.5% CRT met a low-temperature index with equal volume substitution, and the six gradations obtained by unequal volume replacement with 2% CRT complied with the requirements of a skeleton dense texture. When the substitution ratio was 1.5 and 0.5, the high-temperature performance was better. In addition, when the substitution ratio was 0.5, the flexural strain energy density was the highest and the low-temperature performance was the best. Including considerations of economic benefits, it is recommended that the CRT content be 2% and the substitution ratio be 0.5.