If you want to close a Disqus account, you can easily do that in the Settings page of your account.
I’ll show you below with pictures how I managed to remove my profile (using a desktop computer):
1 Go to disqus.com
and login to your account with your email and password.
2 Click on the gear icon in the right top corner
and choose Settings.
3 Scroll down and on the bottom you’ll see a Delete button
4 Let them know why you’re leaving
confirm that you want to remove your profile when you’re set to go.
You’ll be redirected to the homepage and your account is gone immediately.
Source screenshots (and thanks to): disqus.com