Highly correlated ab initio wave functions within the UCCSD(T)-F12 approach have been used to map the potential energy surfaces (PESs) describing the reactivity of the CN- (X-1 Sigma(+)) anion with neutral atoms present in interstellar media (F, Cl, O, and S). With the H atom, for comparison, the reaction [CN-((1)Sigma(+)) + H(S-2)] evolves along the PES of the X-2 Sigma(+) electronic ground state of HCN- (or HNC-) until the crossing with the X-1 Sigma(+) electronic ground state of HCN (or HNC), where electron detachment occurs. The process is rather similar to the two halogen atoms F and Cl, with some differences due to the larger electron affinity of the halogens, making possible the existence of ClCN- in a (2)Sigma(+) state. The reaction of CN- with O and S atoms proceeds via a multistep mechanism. The lowest electronic state at long distance, the 3 Pi state arising from the [CN-(1 Sigma(+)) + O/S(P-3)] reaction channel, does not correlate with the X-1 Sigma(+) ground state of the XCN- anion (X = O or S). This (3)Pi state and its bent components cross at medium R-XC (R-XN) distances the X-1 Sigma(+) ground state of XCN- or XNC-, and at shorter distances the X-2 Pi state of the neutral XCN or XNC where the extra electron can detach. With both O and S atoms, it is shown that the spin-orbit couplings can efficiently lead the [CN-(1 Sigma(+)) + O/S(P-3)] reaction toward the stable X-1 Sigma(+) ground state of XCN- and XNC-.