We have developed an experimental technique to study charge-and energy-flow processes in sub-eV collisions between oppositely charged, internally cold, ions of atoms, molecules, and clusters. Two ion beams are stored in separate rings of the cryogenic ion-beam storage facility DESIREE, and merged in a common straight section where a set of biased drift tubes is used to control the center-of-mass collision energy locally in fine steps. Here, we present measurements on mutual neutralization between Li + and D − where a time-sensitive imaging-detector system is used to measure the three-dimensional distance between the neutral Li and D atoms as they reach the detector. This scheme allows for direct measurements of kinetic-energy releases, and here it reveals separate populations of the 3s state and the (3p + 3d) states in neutral Li while the D atom is left in its ground state 1s. The branching fraction of the 3s final state is measured to be 57.8 ± 0.7% at a center-of-mass collision energy of 78 ± 13 meV. The technique paves the way for studies of charge-, energy-, and mass-transfer reactions in single collisions involving molecular and cluster ions in well-defined quantum states.