“And an ox or sheep; it and its child you may not slaughter on one day!” (Vayikra 22:28)
It is a negative commandment that one may not slaughter an animal and its child on the same day, whether it is an offering or a normal animal, as it says “It and its child you may not slaughter on one day!”.
Amongst the roots of this commandment are that a person should consider the supervision of Hashem over all of the living creatures, and that through the above supervision the world continues to exist. It is therefore important that no species should become extinct through all the days of the world, and we have therefore been commanded not to cut off root and branch together, to remind us of this supervision. On a more basic level we can also say that it is to fix in our hearts the character trait of mercy, and to keep far away from sadism and cruelty which are bad character traits. It is therefore self-understood that even though Hashem allowed us to kill living creatures for our own sustenance, he nevertheless commanded us not to kill an animal and its child on the same day, to fix pity in our hearts.
This commandment applies to men and to women, in all places and at all times.