We utilize ultrafast time-resolved terahertz (THz) spectroscopy as a direct, sensitive, and non-contact all-optical probe to investigate the hot-carrier relaxation and cooling dynamics of buckled epitaxial graphene. This special form of graphene is grown epitaxially on nitrogen-seeded single-crystal silicon carbide (SiC(000 1 ï¿½)) substrates by thermal decomposition of Si atoms. The pre-deposited interfacial nitrogen atoms pin the first graphene layer to the SiC substrate, and cause it and subsequent graphene layers to buckle into nanoscale folds, which opens an energy gap of up to ∼0.7 eV. We observe a remarkable increase of up to two orders of magnitude in the relaxation rate of the THz carrier dynamics of this semiconducting form of epitaxial graphene relative to pristine epitaxial graphene, which we attribute to a large enhancement of the optical-phonon-mediated carrier cooling and recombination over a wide range of electron temperatures due to the finite bandgap. Our results suggest that the introduced bandgap is spatially non-homogenous, with local values close to the optical phonon energy of ∼200 meV, which allows the conduction and the valence band to be bridged by optical phonon emission. We also demonstrate that carrier relaxation times can be modified by orders of magnitude by careful bandgap engineering, which could find application in novel graphene-based devices that incorporate both metallic and semiconducting forms of graphene.