For 175 million years, Mother Nature continues to perfect the development and use of placentas for mammals. Modern obstetrics has intervened by creating a routine procedure of clamping and cutting the cord immediately after birth takes place.
If the placenta is still working while the baby is getting to know the world outside the womb, it would ensure that the baby has sufficient oxygen while allowing him or her to get used to breathing on its own. Delayed cord clamping (approx. 5 minutes) allows the baby to receive all of the available nutrient rich blood that is rightfully theirs. Ask your doctor if there is a risk in waiting to cut the cord until pulsation has stopped on its own.
Dr. Nicholas Fogelson runs an informational blog and podcast called Academic OB/GYN. In his below video he shows the birth of kittens, a horse, and an orangutan to show that other land mammals don't clamp the umbilical cord and aren't concerned about immediate separation. Take a look!