Atomic defects have a significant impact on the low-energy properties of graphene systems. By means of first-principles calculations and tight-binding models we provide evidence that chemical impurities modify both the normal and the superconducting states of twisted bilayer graphene. A single hydrogen atom attached to the bilayer surface yields a triple-point crossing, whereas self-doping and threefold symmetry breaking are created by a vacant site. Both types of defects lead to time-reversal symmetry breaking and the creation of local magnetic moments. Hydrogen-induced magnetism is found to exist also at the doping levels where superconductivity appears in magic-angle graphene superlattices. As a result, the coexistence of superconducting order and defect-induced magnetism yields in-gap Yu-Shiba-Rusinov excitations in magic-angle twisted bilayer graphene.