It really depends on what you want to do, where the door is located and if you care deeply how it looks.
If it's a front door and the chewed part is facing the street where everyone can see it, then by all means, replace it. You want your house to look nice and be a plus and a benefit to the neighborhood.
If it's a back door or a side door that no one can see or is at least out of the way, then have a go at repairing it.
The options for repair are many, depending on your skill level and what you'll settle for in terms of "repair." It could be something as simple as a scrap piece of plywood or even sheet metal nailed or screwed over the hole. If you want to get really creative, you can cut some short boards and create a design, (diamond, herring bone, etc). You'll not only cover the hole, but have fun with the project and end up making something cool you can talk about.
As I see it, especially if it's a back door, you really have nothing to loose in trying to repair it - especially if you have some scraps laying around. It could be a neat Saturday project. Worse case would be you waste some time experimenting and still end up buying a door - so what - have fun and good luck.