You're not alone. Many Taiji (also spelled T'ai Chi) practitioners are not interested in the esoteric, mystical topics that often come along for the ride. They want practical, real skill that can be demonstrated on a resisting opponent.
Trouble is, finding a teacher who can show you this is rare. About 99% of all taiji teachers teach a version of taiji that is primarily oriented towards health and qigong. They will answer questions about the fighting applications of taiji incorrectly, because their teacher never taught them it. They've had to essentially guess at it or pick it up from folklore and whatever they've read or watched on the internet. But they won't tell you that, because they want to save face.
The reason for this is due to the fact that taiji started off as a kind of secret martial art. It was closely guarded by the Chen family (the founders of the art) in China. They doled it out in tiny amounts to those who paid for the knowledge. Like every other martial family in China, that was how they made money. They withheld the knowledge to ensure their family could provide for themselves. So it was never taught in public, only behind closed doors.
Then, as oral tradition tells us, Yang Lu-chan would observe some Taiji training from a crack in the wall. And he would later go on to be accepted as a student of Chen taiji. But, he was forbidden from teaching the martial art aspects to the public. Instead, he taught it as a "health" and meditation form, without any real explanation of what was going on martially. From this came most people doing taiji we see today. Which is why when you go to a taiji school, you may walk away thinking that what they teach is fantasy and unrealistic for actual fighting. Because it is, and they don't know better.
I trained in Wu style first for a year. Then I trained in Yang style for a year and a half or so. I thought I knew what taiji was. But then I met up with a Chen style taiji practitioner who taught me more in just 30 minutes than anything I learned before. It was transformative. Suddenly everything made sense. I could feel it first hand for the first time. And I realized that my previous Wu and Yang style groups had people in them who were training for 20 years and still didn't know the first thing about it!
Please read the following two links, where I go over some of the concepts of taiji and what's really going on it:
How is Tai Chi different as a martial art in terms of self defense/combat?
How long should the Tai Chi basic 24 form take?
The biggest take-away from the links above is that taiji is an internal art, which means that stuff is going on inside of the body that you can't see very easily. It's not mystical. It's not about chi. It's about the body and using it in a different way from external styles.
Now, how you use that stuff in fighting is that you need to be sparring with it. Taiji has the concept of push-hands practice first. In push-hands practice, you learn to apply internal mechanics on a moving, resisting opponent. But there are some rules that limit you from doing just anything. With more competitive practitioners, it resembles judo.
Sparring is also something that takes place in taiji training. It's different from push-hands. In sparring, you have less rules. It's more "anything goes" than push-hands. So this is where you get good at the boxing aspects of it, where people are defending against punches and kicks while also having to deal with grappling, joint locking, and throws.
Although it does depend on your instructor, traditionally you're not going to get to the level where you can even begin sparring until you've spent almost a decade or longer training everything else before that. It's because internal martial arts require a lot more concentration and attention to details.
In external arts, it's very easy. You can watch stuff and repeat what you see. But with internal arts, it's what you don't see that's important. That requires a patient student and instructor. It can take years to build a good foundation.
One of the basic principles of taiji is that you're never extended in any direction. You want all your joints to be a neutral position, neither fully extended or retracted. This is because if a joint is locked, it can't adapt to forces. If your opponent pushes on you, having your joints perfectly neutral means they can easily adapt to those forces in whichever direction the force is coming from. It's when your joints are locked that you can't adapt. It will cause you to become unbalanced and fall.
And that's basically taiji's main defense and offense strategy. It's trying to remain neutral at all times while simultaneously looking to unbalance ones opponent by making them extend their joints too far. Once their opponent is in a vulnerable state, they can unbalance and throw them.
There are many other concepts in taiji that are applied to fighting. For example, sensing and yielding to pressure. This is known as soft skill. Soft skill is the bread and butter of taiji. Someone pushes on you, but instead of stiffening up and pushing back, you feel the force, you receive it, you give a little to the force, capture it, and redirect it for your own gain. Someone who is not trained will be easy to throw this way. I've personally done it many times in real life in playful and very real self-defense situations. This skill comes from push-hands practice, primarily.
The other day someone asked me about all the different styles I've learned, which one is the most useful? I replied, "Taiji". In just about all situations I've ever been in, I've used taiji primarily, at least at first. It's especially good for when you're not ready to get into a full-on boxing match with someone. You're trying to stop them from hurting you, but you don't want to lay into them with strikes.
Someone I was/am good friends with once got really angry with me and started becoming violent. She was going through some problems in life, and I really had no desire to hurt her. So she started shoving me and grabbing me. She was threatening to punch me, too. I just wiggled out of her holds and stuck to her arms, just like in push-hands practice. She tried punching me, and I just controlled that arm and deflected it just enough that it barely grazed me. And while I was doing that, I was causing her to become unbalanced. It really frustrated and confused her. Eventually I saw she was vulnerable and off balance, so I gave her a tiny bit of force that caused her to fall a little and to realize that she could not do anything to me. That's when she just gave up.
I've done that with a bunch of others in my past. Their reactions are quite priceless when they realize they're only making themselves more unbalanced and can't harm me.
There have been others with more weight and more strength, though. Men. They aren't as easy to deal with. You have a small window of time where taiji push-hands can work. After that, you better switch yourself on and get ready for a real fight. Most taiji students never reach that level of training to be able to fight for real with it. I never got to that point, either. It's there in the advanced stages of training, but we're talking 10-20 years of training before you start, with a good instructor. You're better off learning boxing, muay-thai, BJJ, wrestling, Judo, etc. for that, until you can get to that level in taiji.
But that aside, like I said, most of what I've used successfully in the past has been taiji. And it's not fighting. It's more like some useful concepts, at least at first until you get to be good enough to start sparring with it. But those concepts are great. You won't know that until you've had a chance to test it yourself in real life. It won't win real fights by itself, but most situations we get into in life aren't "real fights". They're encounters, usually with people we know and don't necessarily need to fight full-on. And in those situations, taiji is perfect. It's going to frustrate them and cause them to give up. That's the best possible outcome in those cases. It's not about winning.
Hope that helps.