To cancel the Apple Music subscription (or any subscription through Apple/iTunes), go to your subscription settings, select the subscription, then select Cancel Subscription. Then confirm in the Confirm Cancelation pop-up.
View, change, or cancel your subscriptions - Apple Support
Removing the payment method will not work when you have active subscriptions. You first have to cancel subscriptions, then you can change payment methods. It is about the correct order.
Not making use of a subscription service doesn’t change your obligation to pay the agreed fees. If the service is not something that you want, then you can cancel the subscription at any time.