When should the animal be skinned?
About skinning the animal, the Shariah says that the animal should be skinned after it has become completely lifeless and the body of the animal becomes completely still. Thus, it is given in the Hadith:
It is narrated on the authority of Hadhrat Makhul (May Allah be well pleased with him) that when the Holy Prophet (Sallallahu alaihi wa sallam) slaughtered an animal, He would neither sever the head nor skin the animal until it became completely lifeless.
(Mabsut Sarkhsi, Vol. 11, Pg. No. 249)
To start skinning the animal before this is Makruh (Undesirable).
As mentioned in Fatawa A’alamgiri:
(Fatawa A’alamgiri, Vol. 5, Pg No. 300)