Numerical models of magmatism and mantle convection beneath a stagnant lithosphere are presented to understand how water affects Martian mantle evolution. Magmatism is modeled as an upward permeable flow of the basaltic magma generated by decompression melting. First, a global partially molten layer (GPML) develops and generates a basaltic crust, a layer of compositionally buoyant residue of melt extraction in the uppermost mantle, and a denser layer with a higher content of the basaltic component in the deep-mantle. The GPML extracts most of the water initially contained in the upper layer, but some water remains in the lower layer of the mantle. Subsequently, hot plumes ascend from the lower layer to induce magmatism. The water allows plume magmatism to continue for a long duration, up to 5 Gyr depending on the initial water content and the detail of the initial temperature distribution in the mantle, provided that the mantle is initially not too hot just after planetary formation. The plume magmatism is sufficiently active to cause significant crustal growth and dehydration of the crust and mantle in the early evolutionary stage when the internal heating is strong; the amount of extracted water is equivalent to a water layer of up to several hundred meters in depth. Water can also enhance the extraction of heat producing elements (HPEs) from the mantle, reduce the heat flux from the mantle to the crust, and make the lithosphere thicker. Both crustal growth and dehydration eventually subside as the HPEs decay.