Any apoptotic process in a mesenchymal cell. A mesenchymal cell is a loosely associated cell that is part of the connective tissue in an organism. Mesenchymal cells give rise to more mature connective tissue cell types. [ http://purl.obolibrary.org/obo/CL_0000134 GOC:mtg_apoptosis http://www.ncbi.nlm.nih.gov/pubmed/18231833 GOC:yaf ]