And all you need is a USB card reader.
Here's the official line: downloaded Wii U software can't be saved to or played off of an SD card.
Unofficially, though, playing and saving Wii U games to an SD card is entirely possible.
One plucky Wii U user has found a simple workaround to enable data to be saved and accessed via an SD card - and all you need is a cheap USB card reader.
By plugging an SD card into the USB card reader, and connecting the card reader to the console, the Wii U treats the SD card as a standard USB drive, therefore allowing players to transfer and play software directly to/from their SD card.
You can take a look at the process in the video at the bottom of the page.
Of course, this workaround isn't officially supported by Nintendo and could well be patched out in a future firmware update. But for now, if you've got some SD cards lying around, this could save you from having to shell out for an expensive external hard drive.