The annealing of a Cu(4.5at.% Mg)/$SiO_2$/Si structure in ambient $O_2$, at 10 mTorr, and $300-500^{circ}C$, allows for the outdiffusion of the Mg to the Cu surface, forming a thin MgO (15 nm) layer on the surface. The surface MgO layer was patterned, and successfully served as a hard mask, for the subsequent dry etching of the underlying Mg-depleted Cu films using an $O_2$ plasma and hexafluoroacetylacetone [H(hfac)] chemistry. The resultant MgO/Cu structure, with a taper slope of about $30^{circ}C$ shows the feasibility of the dry etching of Cu(Mg) alloy films using a surface MgO mask scheme. A dry-etched Cu(4.5at.% Mg) gate a-Si:H TFT has a field effect mobility of 0.86 $ extrm{cm}^2$/Vs, a subthreshold swing of 1.08 V/dec, and a threshold voltage of 5.7 V. A novel process for the dry etching of Cu(Mg) alloy films, which eliminates the use of a hard mask, such as Ti, and results in a reduction in the process steps is reported for the first time in this work.