By studying M-theory on singular non-compact special holonomy spaces X we demonstrate, via a process of cutting and gluing of singularities that extend to the boundary of X, the appearance of 0-form, 1-form and 2-group symmetries in the resulting supersymmetric quantum field theory. We study the fate of these symmetries when these spaces become compact by employing sophisticated gluing techniques. We highlight prototype examples with spaces X being elliptically fibered Calabi-Yau manifolds, which are dual to F-theory constructions. There we can compare obtained results to previous studies, encoded in the arithmetic structure of elliptic fibration.