In the presented paper, we studied bilayer CVD graphene transferred to a langasite substrate and irradiated with a focused electron beam through a layer of polymethyl methacrylate (PMMA). Changes in the Raman spectra and an increase in the electrical resistance of bigraphene after irradiation indicate a local phase transition associated with graphene diamondization. The results are explained in the framework of the theory of a chemically induced phase transition of bilayer graphene to diamane, which can be associated with the release of hydrogen and oxygen atoms from PMMA and langasite due to the “knock-on” effect, respectively, upon irradiation of the structure with an electron beam. Theoretical calculations of the modified structure of bigraphene on langasite and the experimental evaluation of sp3-hybridized carbon fraction indicate the formation of diamane nanoclusters in the bigraphene irradiated regions. This result can be considered as the first realization of local tunable bilayer graphene diamondization.