I believe that you need to actually install it with zero-length text in order to completely clear it, I'm not sure why this is necessary, but this code works:
clipboard = gtk_clipboard_get(GDK_SELECTION_PRIMARY);
gtk_clipboard_clear(clipboard);
gtk_clipboard_set_text(clipboard, "", 0);
clipboard = gtk_clipboard_get(GDK_SELECTION_CLIPBOARD);
gtk_clipboard_clear(clipboard);
gtk_clipboard_set_text(clipboard, "", 0);
, GTK + X11, " ", GTK (GDK_SELECTION_CLIPBOARD) X11 (GDK_SELECTION_PRIMARY). Windows, GDK_SELECTION_PRIMARY, , .