Nearly all nanomedical applications of dendrimer-like soft nanoparticles rely on the functionality of attached ligands. Understanding how the ligands interact with the receptors in cell membrane and its further effect on the cellular uptake of dendrimer-like soft nanoparticles is thereby a key issue for their better application in nanomedicine. However, the essential mechanism and detailed kinetics for the ligand-receptor interaction-mediated transmembrane transport of such unconventional nanoparticles remain poorly elucidated. Here, using coarse-grained simulations, we present the very first study of molecular mechanism and kinetics behaviors for the transmembrane transport of dendrimer-like soft nanoparticles conjugated with ligands. A phase diagram of interaction states is constructed through examining ligand densities and membrane tensions that allows us to identify novel endocytosis mechanisms featured by the direct wrapping and the penetration-extraction vesiculation. The results provide an in-depth insight into the diffusivity of receptors and dendrimer in the membrane plane and demonstrate how the ligand density influences receptor diffusion and uptake kinetics. It is interesting to find that the ligand-conjugated dendrimers present superdiffusive behaviors on a membrane, which is revealed to be driven by the random fluctuation dynamics of the membrane. The findings facilitate our understanding of some recent experimental observations and could establish fundamental principles for the future development of such important nanomaterials for widespread nanomedical applications.