A similar report to that of the one who bit (another man) and his from tooth fell out was narrated from Ibn Ya'la from his father, in which the Prophet said:"There is no Diyah for you."
أَخْبَرَنَا سُوَيْدُ بْنُ نَصْرٍ، فِي حَدِيثِ عَبْدِ اللَّهِ بْنِ الْمُبَارَكِ عَنْ شُعْبَةَ، عَنْ قَتَادَةَ، عَنْ عَطَاءٍ، عَنِ ابْنِ يَعْلَى، عَنْ أَبِيهِ، بِمِثْلِ الَّذِي عَضَّ فَنَدَرَتْ ثَنِيَّتُهُ أَنَّ النَّبِيَّ صلى الله عليه وسلم قَالَ " لاَ دِيَةَ لَكَ " .
Nesai
The Book of Oaths (qasamah), Retaliation and Blood Money • Hadith 4770