In my opinion, hitting a female in the United States would be criminal assault, and domestic abuse if it happens in a marriage. And I agree that it should be illegal to physically violate a woman.
In case a Christian man's girlfriend is wrong somehow, I offer that his Biblical role is to be her good example to help her do better, and his role is to minister for her to be restored spiritually, like we have in Galatians 6:1 >
"Brethren, if a man is overtaken in any trespass, you who are spiritual restore such a one in a spirit of gentleness, considering yourself lest you also be tempted." (Galatians 6:1)
I see this means how an individual who is "spiritual" has power of God to restore any person out of "any trespass". So, this is the focus to have in dealing with however a girlfriend might be wrong. And we need to have our mature older Christians who feed us their example of how to relate. So, it is important that you do not isolate yourself only or mainly with your girlfriend, in how you share and might have the right kind of discipline.
"He can have compassion on those who are ignorant and going astray, since he himself is also subject to weakness." (Hebrews 5:2)
So, in case your first focus is about hitting her, and controlling her, and being angry, this is not Biblical, I would say. Start with compassion and how with God in prayer we are able to bless someone.
Also, in case you do have some sort of agreement that there can be need for discipline of certain wrong things, then the man needs to take the lead in how to be disciplined. Or else he is not a leader.
"nor as being lords over those entrusted to you, but being examples to the flock." (1 Peter 5:3)
Controlling and lording yourself over her is not leading by example.
You say she might need her cell phone to go on time out. Well, if you really mean she is not giving you the attention that you want . . . discipline must not be for selfish reasons. Love does not have us only using any other person; so if you are trying to get her to cooperate with you so you can use her . . . this is not loving her. And physical pain is certainly not God's way of getting us to obey Him. Yes, He has used pain on wrong people, but that did not change their character so they became His way in obeying and loving.
We need ministry of restoration in which God is changing our character so we are and we love more like Jesus. The focus of true discipline is how we become and we love like Jesus >
"And walk in love, as Christ also has loved us and given Himself for us, an offering and a sacrifice to God for a sweet-smelling aroma." (Ephesians 5:2)
The man taking the lead, then, needs to reveal how he has sinned, even in secret, including in his imagination; then he gets disciplined however has been agreed . . . with him taking the lead if he is supposed to be the leader.
But the true discipline, I think, is revealed through Hebrews 12:4-14. God alone is able to do this. So, if I am boasting how I could discipline my sweetie . . . uh-uh!!
By the way > when those people in John chapter eight brought the adulteress to Jesus, who did Jesus first deal with, about who had been sinning? Not the woman, but the men. And Jesus did not physically violate her, but He did what could help her to live better.