Mitochondrial electrogenic aspartate/glutamate antiporter that favors efflux of aspartate and entry of glutamate and proton within the mitochondria as part of the malate-aspartate shuttle (PubMed:11566871, PubMed:38937634, PubMed:38945283, PubMed:39419476). Substrate exchange across the membrane occurs consecutively with one substrate being transported first, then dissociating from the substrate binding site before the second substrate binds for transport in the opposite direction (PubMed:38937634). Also mediates the uptake of L- cysteinesulfinate (3-sulfino-L-alanine) by mitochondria in exchange for L-glutamate and proton (PubMed:11566871). Can also exchange L- cysteinesulfinate with aspartate in their anionic form without any proton translocation (PubMed:11566871). Lacks transport activity towards gamma-aminobutyric acid (GABA) (PubMed:38945283). {ECO:0000269|PubMed:11566871, ECO:0000269|PubMed:38937634, ECO:0000269|PubMed:38945283, ECO:0000269|PubMed:39419476}. This is the function of ENSG00000004864 (SLC25A13, solute carrier family 25 member 13).