Residents were shocked, saying the suspect was bold enough to return while police were on the scene to allegedly steal the victim's car.
The NYPD released the video, which shows the man punching the woman. And as she hits the ground, the suspect is seen running off with the purse.
Police say the suspect is described as a black man, approximately 5-foot-10, wearing long black shorts, a white shirt and a backpack.
The victim is said to be recovering with a swollen and bruised face.
Eyewitness News is told the victim is a teacher at the school where the attack took place.
Anyone with information is asked to call Crimestoppers at 1-800-577-TIPS.