A prostration when reciting Sad is not one of those which are divinely commanded, but I have seen Messenger of Allah ﷺ prostrate himself.  

لَيْسَ { ص } مِنْ عَزَائِمِ السُّجُودِ وَقَدْ رَأَيْتُ رَسُولَ اللَّهِ ﷺ يَسْجُدُ فِيهَا  

The Messenger of Allah ﷺ recited surah Sad on the pulpit. When he reached the place of prostration (in the surah), he descended and prostrated himself and the people prostrated with him. When the next day came, he recited it. When he reached the place of prostration (in the surah), the people became ready for prostration. Thereupon the Messenger of Allah ﷺ said: This is the repentance of a Prophet ; but I saw you being ready for prostration. So he descended and prostrated himself and the people prostrated along with him.  

أَنَّهُ قَالَ قَرَأَ رَسُولُ اللَّهِ ﷺ وَهُوَ عَلَى الْمِنْبَرِ { ص } فَلَمَّا بَلَغَ السَّجْدَةَ نَزَلَ فَسَجَدَ وَسَجَدَ النَّاسُ مَعَهُ فَلَمَّا كَانَ يَوْمٌ آخَرُ قَرَأَهَا فَلَمَّا بَلَغَ السَّجْدَةَ تَشَزَّنَ النَّاسُ لِلسُّجُودِ فَقَالَ النَّبِيُّ ﷺ إِنَّمَا هِيَ تَوْبَةُ نَبِيٍّ وَلَكِنِّي رَأَيْتُكُمْ تَشَزَّنْتُمْ لِلسُّجُودِ فَنَزَلَ فَسَجَدَ وَسَجَدُوا