Place the shower pan onto the floor where it will be installed. Trace where the drain hole lies on the subfloor with a marker by making a circle. The only time you should need to cut through the subfloor to replace the shower drain is if a new pan is being added and the new drain hole doesn't match up with the old one. Otherwise, a new drain should fit right through the subfloor where the old one was.
Compare your new drain with the size of the hole you've drawn onto the subfloor. Make sure your drain fits that hole before continuing. If you're not sure, slide the drain through the hole in the shower pan and screw it in as a test to verify the size is correct.
Press a reciprocating saw against the subfloor where you drew your circle. Cut a straight line across the diameter of the subfloor with the saw. Wear safety goggles to protect yourself against debris. Use a toothed saw blade for a wood subfloor and an abrasive or a diamond saw blade for a concrete subfloor.
Saw another line across the circle to form an X with the original line you just cut. Hammer out the subfloor pieces with a rubber mallet to create the opening for the new drain. Make additional cuts as needed in the circle to further weaken the material to create the full hole.