Fast Dial isn't cutting miniatures. It's just rounded corners apply to invisible thumbnail title.
To solve the problem, you can try one of the following approaches:

1. Set Round to zero in Fast Dial preferences (Appearance > Thumbnail). If you want rounded corners, you'll need another approach.
2. Modify fastdial.css file. You need Firefox Developer Version for that.
3. Use Stylish (https://addons.mozilla.org/firefox/addon/stylish/) addon:
   1. Install addon and go to the Styles tab.
   2. click to create a new style
   3. set style name to be "Fast Dial: no titles".
   4. set content of the style to be:
      @-moz-document url-prefix(chrome://fastdial/content/fastdial.html) {
          .title {
              display: none;
          }
          .body, .background {
              bottom: 0px;
          }
      }
   5. save style and open Fast Dial page to test. You're done.