The Wii U has the ability to take in game screenshots, but not in the way that you likely want it to. As of right now (January 2016) the Wii U is able to take a screenshot of the current game. To take a screenshot you need to press the home button on the controller and on the menu that appears on the controllers screen, click “Miiverse”. This will load up the Miiverse app.
When the app has loaded up you will see a thumbnail of the game that you are playing and you can post or save this picture to your miiverse account. Unfortunately this is all that you can do with the screenshot at the moment. If you would like to save this to an SD card…you can’t.
Seems like a major oversight that something like this can’t be done with a modern game console and even this late after the release of the console it still can’t be done. I’m sure Nintendo will patch this in some day, but for now there is nothing you can do to directly copy these screenshots onto an external media source.