The dynamics of the adsorption and evolution of fluorinated C60F18 fullerene molecules on the Cu(001) surface are studied by real-time ultra-high vacuum scanning tunneling microscopy. Fluorinated fullerene molecules are shown to decompose with time on the Cu(001) surface transforming to C60 molecules. The decay rate depends on the initial molecular coverage. The rapid decay of fluorinated fullerene molecules is observed when the coverage is no higher than 0.2 single layers. As a result, two-dimensional islands consisting of pure C60 molecules are formed on the Cu(001) surface. 2D islands consisting of fluorinated fullerene molecules are formed when the initial molecular coverage is higher than 0.5 single layers. The molecules inside these islands also tend to decompose with time. It is found experimentally that fluorine atoms are removed completely from the initial C60F18 molecules adsorbed on the Cu(001) surface after 250 h when the initial molecular coverage is 0.6 single layers.