Right click on the style in the Quick Style Gallery
Click on Modify
In the bottom left corner of the popup click on the Format menu
Click on Language
Select the check box "Do not check spelling or grammar" (be sure to select a language first!)
Click OK on the Language dialog box
Click OK on the Modify Style dialog box
The spell checking will not immediately disappear. But new words you create in that style will not be checked. Restarting Word works too.
