Although it might look close as the crow flies, by road Punta Cana is almost as far as you can get from Samana from any airport in the island, except maybe Barahona.
You need to drive towards the capital (3hrs) and take the new highway to Samana (2hrs) between Santo Domingo airport and the city. If you're using public transport and have a sense of adventure, take local buses to Sabana de la Mar (via Higuey and El Seibo) and cross Samana Bay on the ferry (foot passengers, bicycles, mules, donkeys and motorbikes only).