Answer
✅Answer: Please pay attention to the following narrations:
1 عَنِ النَّوْفَلِيِّ عَنِ السَّكُونِيِّ عَنْ أَبِي عَبْدِ اللَّهِ قَالَ: تَلْبِيَةُ الْأَخْرَسِ وَ تَشَهُّدُهُ وَ قِرَاءَتُهُ الْقُرْآنَ فِي الصَّلَاةِ تَحْرِيكُ لِسَانِهِ وَ إِشَارَتُهُ بِإِصْبَعِهِ.
📚Al-Kafi, Vol. 3, p. 315
Imam Sadiq (peace be upon him) said: The 'talbiya' of a mute person and his 'tashahhud' and recitation of the Qur'an in prayer are by moving his tongue and pointing with his finger!
2 عَنْ مَسْعَدَةَ بْنِ صَدَقَةَ قَالَ سَمِعْتُ جَعْفَرَ بْنَ مُحَمَّدٍ يَقُولُ إِنَّكَ قَدْ تَرَى مِنَ الْمُحَرَّمِ مِنَ الْعَجَمِ لَا يُرَادُ مِنْهُ مَا يُرَادُ مِنَ الْعَالِمِ الْفَصِيحِ وَ كَذَلِكَ الْأَخْرَسُ فِي الْقِرَاءَةِ فِي الصَّلَاةِ وَ التَّشَهُّدِ وَ مَا أَشْبَهَ ذَلِكَ فَهَذَا بِمَنْزِلَةِ الْعَجَمِ وَ الْمُحَرَّمِ لَا يُرَادُ مِنْهُ مَا يُرَادُ مِنَ الْعَاقِلِ الْمُتَكَلِّمِ الْفَصِيحِ
📚Qurb al-Isnad, 24
Mas'ada said: I heard Imam Sadiq (peace be upon him) say: Indeed, you see that what is required of an eloquent scholar is not required of a non-Arab person whose training and practice (in learning Arabic) are not yet complete, and likewise is the mute person in his recitation in prayer and 'tashahhud' and the like. So this person is also like the non-Arab, and what is required of an eloquent speaker is not required of one whose training and practice are not yet complete!
3 أَخْبَرَنَا عَبْدُ اللَّهِ أَخْبَرَنَا مُحَمَّدٌ حَدَّثَنِي مُوسَى قَالَ حَدَّثَنَا أَبِي عَنْ أَبِيهِ عَنْ جَدِّهِ جَعْفَرِ بْنِ مُحَمَّدٍ عَنْ أَبِيهِ عَنْ جَدِّهِ عَلِيِّ بْنِ الْحُسَيْنِ عَنْ أَبِيهِ عَنْ عَلِيٍّ قَالَ: تَلْبِيَةُ الْأَخْرَسِ وَ قِرَاءَتُهُ الْقُرْآنَ وَ تَشْهَدُهُ فِي الصَّلَاةِ يُجْزِيهِ تَحْرِيكُ لِسَانِهِ (وَ إِشَارَتُهُ) بِإِصْبَعِهِ
📚Al-Ja'fariyat, p. 70
Ali (peace be upon him) said: The 'talbiya' (saying 'labbayka Allahumma labbayk') of a mute person in 'ihram' and his recitation of the Qur'an and his 'tashahhud' in his prayer are sufficient by the movement of his tongue (and his pointing) with his finger!
✅ It is clear that a mute person performs his recitation, 'tashahhud', and other prayers by moving his tongue and pointing with his finger, and in this way he performs his prayer.
اللَّهُمَّ صَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ
وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ