Catalyzes the attachment of aspartate to tRNA(Asp) in a two- step reaction: aspartate is first activated by ATP to form Asp-AMP and then transferred to the acceptor end of tRNA(Asp). {ECO:0000269|PubMed:15779907, ECO:0000269|PubMed:23275545, ECO:0000269|PubMed:40814755}. This is the function of ENSG00000117593 (DARS2, aspartyl-tRNA synthetase 2, mitochondrial).