ABSTRACT During the past decade, the dynamical importance of magnetic fields in molecular clouds has been increasingly recognized, as observational evidence has accumulated. However, how a magnetic field affects star formation is still unclear. Typical star formation models still treat a magnetic fields as an isotropic pressure, ignoring the fundamental property of dynamically important magnetic fields: their direction. This study builds on our previous work, which demonstrated how the mean magnetic field orientation relative to the global cloud elongation can affect cloud fragmentation. After the linear mass distribution reported earlier, we show here that the mass cumulative function (MCF) of a cloud is also regulated by the field orientation. A cloud elongated closer to the field direction tends to have a shallower MCF: in other words, a higher portion of the gas is at high density. The evidence is consistent with our understanding of the bimodal star formation efficiency discovered earlier, which is also correlated with the field orientation.