Fruit textural characteristics can affect the storage, transportation, and processing of plum (Prunus salicina Lindl) in commercial production. We analyzed 23 plum cultivars with marked differences in fruit traits. Basic physicochemical indicators and textural characteristics of the fruits were determined using puncture testing and texture profile analysis. Furthermore, through the combined application of cluster analysis and principal component analysis, the indexes were simplified to three relatively independent dimensions, comprehensively reflecting the hardness, size, and flexibility of plum fruit. Our results show a high positive correlation among textural characteristics such as hardness, springiness, gumminess, and chewiness, whereas toughness and brittleness were negatively correlated. In addition, physicochemical properties were correlated to the texture traits. The weight and size of the plum fruit were related to hardness, adhesiveness, and chewiness. The soluble solids and water content contributed to the hardness, cohesiveness, and resistance to chewing. Cluster analysis revealed three distinct clusters: Cluster I represented by ‘Meiguihong’ with high hardness and a chewable texture; Cluster II represented by ‘Siyuecui’, ‘Cuimi’, and ‘Qingcui’ with a hard and brittle texture; and Cluster III represented by ‘Jinmi’, ‘Taoli’, and ‘Oishiwase’ with a soft and tough texture. The results of this study provide a significant theoretical foundation for quality evaluation, and classification of plum fruit characteristics, thus providing insights for further breeding of plum varieties.