We introduce the concept of 3D Dirac (Weyl) superconductors (SC), which have protected bulk four (two)-fold nodal points and surface Andreev arcs at zero energy.We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry.Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontrivial.Breaking mirror symmetry may gap Dirac nodes producing a topological SC.Each Dirac node evolves to a nodal ring when inversion-gauge symmetry is broken, whereas it splits into a pair of Weyl nodes when and only when time-reversal symmetry is broken.