The sentence that is punctuated correctly is, "I used the green pen, not the red one, for my homework."
Because the information, "not the red one" is unneccary to understand the meaning of the sentence, it needs to be set apart from the rest of the sentence by commas. In other words, we could just say, "I used the green pen for my homework." and the reader would understand the main idea. However, because we add "not the red one," we include the information between two commas.