Available in all plans.
Yes, you can! There are two ways for doing it:
1. From the alert feed (both for basic and boolean alerts)
Click on a mention in your feed, hover over it and click on the block source button.
2. From the alert edition page
Click on the gear icon that appears when you hover over the alert name, then expand the "Main Information" section and copy paste the URL of the site in the blocked Websites field.
If you are using boolean alert, click on the gear icon that appears when you hover over the alert name, then click on "Edit the query". Click on the "Blocked Websites" tab and copy paste the URL of the website. Then click on "Block". And don't forget to always save your query.