Does canceling service stop AutoPay too?

Yes, your AutoPay enrollment will be canceled after you cancel your services and all outstanding bills are paid. There is no other step you need to take. 

Your AutoPay enrollment will stay active for payment of all of your closing bills from CenturyLink. If you do not want your post-cancellation bills to be automatically paid, you can cancel AutoPay at the time of your service cancellation and pay those final bills using another payment method.

AutoPay on your closing CenturyLink bills

We send your initial closing bill out to you right after your service is canceled. If you're enrolled in AutoPay at the time you cancel your services, that initial closing bill will be paid via your normal AutoPay process.

But you may get a few more bills before your account is completely closed. This is because  additional charges sometimes come in later (e.g., DIRECTV, unreturned equipment), which trigger subsequent bills. If your AutoPay enrollment is still in effect, it will be noted on those bills and paid automatically. Any bills that don't acknowledge your AutoPay enrollment will need to be paid some other way.

The most common charge that surprises customers is an unreturned equipment charge. If equipment is not returned within 30 days of your cancellation date, you will be charged. If your AutoPay is still in effect, those charges will be paid via your AutoPay method. To avoid these unreturned equipment charges, please use the equipment return process within 30 days of your service cancellation.