Hi,
You could disable their user account via the Joomla user manager.
Another option would be to create a user group "can checkout", add it to all the other users, and restrict the payment methods to that "can checkout" user group.
That way, the user wouldn't have any payment method available during the checkout and he wouldn't be able to finish the checkout.
Another way would be to configure an auto loaded coupon restricted to that user with a percentage of -100000%. This would result in a coupon added to the cart of that user which would add a big amount to the cart of the user.
Then, you could set a maximum price in your payment methods so that they don't appear during the checkout because the cart total amount would be too big, and he wouldn't be able to finish the checkout.