Islam does not say anything about that. Ofcourse whipping any human is bad. Thats more a humanistic nature, rather than Islamic view. Islam is more related to spirituality and how to overcome sins.

As a Muslim, I would still keep the following Hadiths in mind. And hitting the face is always forbidden.:
The Prophet (peace and blessings of Allaah be upon him) said: “Allaah is Kind and loves kindness, and He rewards for kindness in a way that He does not reward for harshness or for anything else.” Narrated by Muslim (2593).
The Prophet (peace and blessings of Allaah be upon him) said: “Whoever is deprived of kindness is deprived of goodness.” Narrated by Muslim (2592).
Umar's son (ra) was lashed as a punishment for his crime of drinking alcohol, not for discipline.If I remember, Umar (ra) lashed his son for drinking alcohol till his son died. What does that tell you
From my observation, most of those merciless people, who brutally beat their kids, beat them for worldly things. They smack their kids when they don't obey them like when the kids don't agree to sleep, misbehave (example break something) and cause trouble. Except for those whom Allah has mercy on, not for their deen.