First option, suggested by Destructoid's CEO, Hamza:
Switch to blog style. Just go here: http://www.destructoid.com/user_edit_display.phtml
Honestly, i don't like the blog style, it takes like twice the time to browse through articles.
Second option, suggested by me: 1.
Install Adblock Plus https://adblockplus.org/ 2.
Go to "Add you own filters" and copy and paste these separately in the "+ Add Filter" field and press the ""+ Add Filter" button:
Tested on Opera and Chrome.