A group \(G\) is said to be a mutually \(m\)-permutable product of two subgroups \(H\) and \(K\) if \(G=HK\) and every maximal subgroup of \(H\) permutes with \(K\) and every maximal subgroup of \(K\) permutes with \(H\). In the current paper, the authors investigate the structure of a finite group that is a mutually \(m\)-permutable product of two subgroups under the assumption that its maximal subgroups are totally smooth.