It is important to make the distinction between Turkish/Persian art and Arab art. Arab art is usually focused on geographic shapes and calligraphy, and rarely depicts living things of any kind. In Arab culture depictions of living things were generally more taboo than in other parts of the Muslim world, but it was never really a hard and fast prohibition so there are a few examples of Arab art depicting living things. I hadn't heard of the Pisa Griffin before, but it is definitely a cool example of Arab sculpture. This is just speculation, but maybe the Arabs in Andalusia were influenced by the Berbers (non-Arab natives of north Africa) who were active in the region and it loosened their prohibition of sculpture/other stuff which could be seen as idolatrous. The only other example of Arab sculpture I can find is also in modern-day Spain, [ lions in the court of alhambra ] ( http://en.wikipedia.org/wiki/File:Granada_Alhambra_Fuente_de_los_leones.jpg )

Persian culture is less opposed to depictions of living things and it was common to depict living things in [ Persian Miniatures ] ( http://en.wikipedia.org/wiki/Persian_miniature ) even after the Muslim conquest of Persia. You'll notice that the majority of the depictions of Mohammed in the link you provided are of Persian/Turkish Origin. In terms of sculpture, in Persia there are examples of stone carved reliefs, but I have never heard of sculpture depicting the prophet in particular.

As for why, Muslims are opposed to idolatry. Depictions of the Prophet are seen as promoting idolatry, and statues in particular seem to invite worship. So while images in Persian miniatures may be permitted at times, a statue of the prophet would be totally taboo.