Triple shape memory materials currently have a wide range of applications in aerospace and healthcare, however, the lack of their mechanical properties limits their wider application. In order to overcome the problem of low mechanical properties of the triple shape memory composites, in this study, organoclay (OC), which is low-cost and has an intercalation-type structure, was introduced as a reinforcing phase in a trans-isoprene (TPI) with regular molecular chains and a low-crosslinking low-density polyethylene (LDPE) matrix. TPI/LDPE/OC shape memory composites (SMP) were prepared by melt blending and vulcanized by dynamic vulcanization technique. Since different OC contents have different effects on the properties of the composites, it is particularly important to select the appropriate OC content. A series of experiments were conducted to reveal the effect of OC content on the mechanical and shape memory properties of TPI/LDPE/OC composites. The results show that OC can form a stable and homogeneous intercalation structure in the composites when the OC incorporation amount is 2 phr, and the mechanical properties and triple shape memory properties of the composites are optimized. This study demonstrates that OC can improve the crystallinity and cross-linking of TPI/LDPE composites, thus providing potential value for the study of multiple shape memory material applications.