You're gonna have a rough time matching color and grain/saw marks, but here goes.
Get a piece of wood that's 10" long and an inch or two wider that the door. Wrap it in plastic wrap. Get wood filler and follow can directions. Apply more than you need to damaged section. Push the plastic wrapped wood against the edge. This will force excess out and give you a relatively smooth edge. Figure out a way to attach the wrapped piece of wood to door - rope it, nail it, or if you have a very wide clamp, clamp it. This is gonna stay in place until filler dries. Next get a spackle knife or putty knife and push down on the excess that has come out when you squeezed the wrapped wood against the edge. This will help fill any voids. Then use the putty knife to smooth any filler so that it's relatively level with the door surface. Many fillers shrink when drying, so it's a good idea not to make it too smooth compared to the surface. After 20 minutes or so take a sharp knife and use the tip to make little slits in this surface so that it has grain/saw marks similar to surrounding area.
Let us know how you make out.
Bob "Boardman" Borders