Sorry, but I don't see how this sport can be done to the glory of God. Why would you hit someone in the fact for the sake of pleasure? I ain't talkin bout self defense, but just brainless hitting. I don't think a Christian should partake in this since God called us to be peacemakers. Once again, not talking about defending others, but there is no reason to do boxing. It is just plan fleshly. Here a good video on this matter:
Your premise starts off with a few false ideas.
Fighters (boxers and mma) are athletes that train their minds and bodies. They study opponents other fighters to understand that fighters strengths and weaknesses. And, if need be, adapt their training as needed. I believe this can be more obvious in mma.
This means their hitting isn't mindless. Good fighters look for openings, know when to block or back off. And in mma it's even trickier as there are more options to watch out for, punches, kicks, taken to the ground, holds, etc...
And you can see the evidence of this special training when they go against people who are untrained. And the reason this usually happens is because they are challenged by cocky people who think what they do is a joke. Or in real life situations.
Whatever the reason I've yet to see a well trained fighter taken down by untrained fighters. In fact the fighters usually take it easy on the challenger and don't give 100% and still beat them effortlessly. So it's not mindless hitting.
The goal isn't about enjoying hurting people, but about competition. Athletes competing, just as in any other sport such as baseball, football, soccer, etc...
Fighters are expected to use restraint when necessary and not doing so can lead to punishments. Or even fan backlash. Continued lack of restraint or cheating can even get you kicked out of an organization.
While it's true some people in these fields may take enjoyment from the actually hurting of others, this mentality is not encouraged among professional organizations. They are viewed as professional athletes and expected to act like it.
But people who enjoy hurting others isn't limited to these kinds of sports. You find such people in every aspect of life.
Good examples of this are videos I've seen of fighters using their skill to take down a criminal and subdue them, usually without striking them if possible.
One I recall a man tried to steal a woman's baby in a public area. She of course began resisting and screaming. People quickly ran to help and got them separated. But people were obviously angry at him and many men were crowding around and the situation seemed to be getting increasingly volatile. A fighter jumped in and subdued the guy on the ground, no hitting, and held him their till police arrived.
His reason? Obviously to ensure the creep didn't try to steal the baby again, but he also saw the crowd was getting riled up and he feared the man may be mobbed and beaten or even killed. So he stepped in to ease the whole situation for everyone's good.
Whether or not God finds these things acceptable, I get the reason to think He doesn't, and it may be true. But for myself I see trained athletes engaging in things they agree to ahead of time and put their lives into training for. If I'm wrong then God will tell me otherwise. Until then I'll not worry about it.