It is widely accepted that coronal magnetic flux ropes are the core structures of large-scale solar eruptive activities, which inflict dramatic impacts on the solarterrestrial system. Previous studies have demonstrated that varying magnetic properties of a coronal flux rope system could result in a catastrophe of the rope, which may trigger solar eruptive activities. Since the total mass of a flux rope also plays an important role in stabilizing the rope, we use 2.5-dimensional magnetohydrodynamic (MHD) numerical simulations in this letter to investigate how a flux rope evolves as its total mass varies. It is found that an unloading process that decreases the total mass of the rope could result in an upward (eruptive) catastrophe in the flux rope system, during which the rope jumps upward and the magnetic energy is released. This indicates that mass unloading processes could initiate the eruption of the flux rope. Moreover, when the system is not too diffusive, there is also a downward (confined) catastrophe that could be caused by mass loading processes, via which the total mass accumulates. The magnetic energy, however, is increased during the downward catastrophe, indicating that mass loading processes could cause confined activities that may contribute to the storage of energy before the onset of coronal eruptions.