I'm the bearer of bad news: Despite what other have suggested, the answer to your question is NO. Lightroom (3,4 and 5) does not support Moving images from SD card.

See P39 of the Lightroom 5 manual:

In the top center of the import window, specify how you want to add the photos to the catalog:

• Copy as DNG Copies camera raw files to the folder you choose and converts them to the Digital Negative (DNG) format.
• Copy Copies the photo files to the folder you choose, including any sidecar files.
• Move Moves the photo files to the folder you choose, including any sidecar files. Files are removed from their current location.
• Add Keeps the photo files in their current location.

Note: The Move and Add options are not available when importing from a camera card.

Having explored a bit on the Mac side, I think I have a way for you to get what you want. It involves the Mac's Image Capture and AutoImporter tools.

The workflow basically runs like this: Use Image Capture app to specify that AutoImporter is to open when the SD card is inserted. You can then configure AutoImporter to move the pictures to a specified folder, and remove the originals from the card. You need to get at the AutoImporter preferences to do this.

Now, when you insert a card with images, they're automatically copied to the desired folder and removed from the card. No user intervention required - and when Autoimporter deletes the originals from the card they are really gone. They're not in Lightroom yet, but that's easy.

Eject the card. Now use Lightroom's importer to move or add the images to the catalog, doing all the clever things that it can do along the way.

Note: I have tested this but don't use this approach for real. I live on the 'bootcamp' side of my Mac, so have the similar problems.