Mycobacteria are intracellular pathogens. So, it causes a TH1 response --> IFN gamma --> Macrophage activation --> Granuloma
IOW Cell-Mediated Immunity ( Macrophages, CD8+ cytotoxic T cells, NK cells) deals with intracellular pathogens.
Same goes with other facultative intracellular pathogens like Listeria, Histoplasma, Leishmania etc
Obligate intracellulars pathogens like viruses, rickettsiae, and chlamydiae are killed by cytotoxic T cells, natural killer cells, ADCC.