Preheat oven to 350°F (180°C). Line a large baking sheet with parchment paper. Slightly oil paper with cooking oil spray. Set it aside.
In a large mixing bowl, stir the sweet potato puree and peanut butter.
Stir in the flour. Start stirring with a wooden spoon, then use your hands to knead the dough. If too dry or crumbly to form a ball, add 1-2 teaspoons of water to bring the ingredients together. If too wet, add a bit more flour. The dough should be tough but hold together in a ball.
Place the dough on a floured surface. Sprinkle a little more flour on top to prevent the dough from sticking to the rolling pin.
Roll the dough ball into a 1/2-inch thickness, and using a dog cookie cutter, cut out bone shapes.
Place the bone-shaped cookies on the prepared cookie sheet. They won't expand while baking but leaving half a thumb of space between each of them makes it easier to remove from the tray later.
Bake for 15 minutes for softer cookies or up to 25 minutes for ultra-crunchy treats. Bake until golden brown, not burnt or too dark.
Cool on a cooling rack immediately.