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Two-dimensional materials, such as graphene and transition metal dichalcogenides, have been considered promising for novel (opto)electronic and energy applications due to their unique properties at the mono- to few-layer limit. A thorough understanding of their carrier dynamics and energy transport behavior is therefore needed. Here, we present ultrafast carrier and energy-transport dynamics observed in sapphire-supported monolayer MoS₂ following photoexcitation, using femtosecond transient reflectivity and ultrafast electron diffraction (UED). In particular, both monolayer MoS₂ and the sapphire substrate were probed by reflection UED, which allows direct monitoring of structural motions at the interface. It is determined that dissipation of the photoexcitation energy undergoes a few steps with their characteristic time constants: ultrafast carrier relaxation and recombination as well as carrier-phonon coupling in MoS₂, energy transport from the monolayer to the substrate on a 10-ps time scale, and slower thermal diffusion in bulk sapphire. Temperature-dependent observations will also be discussed.