Shaykh ʾAbd ar-Razzāq al-Badr (حفظه ٱللّٰه) said,

“If it was permissible to mimic voices then the Companions would have dedicated themselves to mimicking people with beautiful voices. And the Prophet ﷺ had informed that Abū Mūsā al-Ashʾarī (رَضِيَ ٱللّٰهُ عَنهُ) has been given a voice like that of Dāwūd (عَلَيْهِ ٱلسَّلَامُ), due to his beautiful voice and good recitation. And it has not been related that any one from among the Companions (رَضِيَ ٱللّٰهُ عَنهُمْ) or those who succeeded them upon goodness mimiced him (Abū Mūsā). So when they abandoned that, given their diligence to do good, which alludes (to the fact) that this deed is from overburdeing which was invented in the later times. And Allāh knows best.

And in our times, people have appeared who have become known for mimicking voices of famous recitors. To the extent that some of them mimic a number of reciters which is not a small number. And he does not err in mimicking the accent of their voices, and the way of their recitation. Then it is said to him, “Mimic so and so, and so and so” and they listen to his mimicry not the Qurʾān. And perhaps they laugh or are amazed (at it), without there arising any reflection for the Qurʾān. And this is not for what the Book of Allāh the Mighty and Majestic was revealed. And this is not the state of the one who magnifies the Speech of Allāh the Mighty and Majestic.”

Source: at-Tibyān fī-sh-Sharḥi Akhlāqi
Ḥamalati-l-Qurʾān, Pg. 182-183

Translated by Zubayr bin Muḥammad ʾAbbāsī