A: The clamp-on type is unlikely to work because you won't have screen to clamp onto on two sides. You'll need to replace the damaged screen, and then install the pet door. If you're planning to get a dog door that fastens to the screen frame itself then, as long as the pet door frame is larger than the torn out portion you'll very likely to be able to do the install with the screen "as is". This, of course, implies that you have the skill to re-spline the screen to the pet door--a job that isn't particularly easy. You might need to make a trip to the screen shop just to make sure you get a good result.
Screen Mounted Pet Doors for cats and dogs - Moore Pet Supplies
The screen flap needs to be able to close on its own and seal itself. The way to do this is to add weight to the end of the screen flap. Remove the masking tape from the screen and place duct tape along the sides so that it is in the front and the back. Do the same thing with the sides and bottom of the flap. Attach several washers to the bottom of the flap using the metal thread and needle. You want them to hang down from the flap. The needle will easily go through the duct tape. Use the hot glue gun and place a thin line of glue on the back of the magnetic strip. Attach it to the bottom of the screen door. Place a second magnetic strip on the outside of the screen door. The dog can now enter and leave without damaging the screen door.
Pet Doors Screen Door with Pet Door Dog Screen ..
With the masking tape framing out the area for the dog screen door you can now cut it out. Start at the bottom of the screen door and cut across. This will give you enough room to cut the sides of the area you taped off. Do not cut the top of the screen. The goal here is to make a flap out of the current screen. Do not fold the flap up or crease it.
Screen Dog Doors for Large Dogs | Pet Door Store