If you are using your iPhone, iPad or AppleTV as your streaming device, you will need to cancel your DOGTV subscription via the Subscriptions page in the App Store: (App Store > Account > Subscriptions)
You can find detailed instructions here and also below.
Manage your DOGTV subscription
Follow these steps to cancel your DOGTV subscription from your iPhone, iPad, iPod Touch, Mac/PC or AppleTV.
1. Go to Settings > [your name] > iTunes & App Store.
2. Tap your Apple ID at the top of the screen.
3. Tap View Apple ID. You might need to authenticate your Apple ID.
4. Tap Subscriptions
5. Select your DOGTV subscription and 'Cancel Subscription'.