On your Subscription and Billing page, you will find the “Cancel your subscription” section at the bottom of the page. Clicking the ‘Cancel Subscription’ button will cancel your subscription at the end of the billing period that you have already paid for, preventing any further charges.
Once your Subscription is Cancelled:
Your subscription will automatically be reverted back to the Basic ad-supported plan once your paid subscription runs out.
Ads will then begin to appear on your site wherever Disqus is installed.
Cancelling your plan will also clear the current billing information stored.
More information on Subscriptions and Billing may be found here.