For me, martial arts practice has always been very effective at keeping me in the moment and shutting out my worries from the rest of my life. I attribute this to two factors:
1) I really, really love the martial arts and find the details of practice and study fascinating. This makes it easy to immerse myself in what I'm doing.
2) The nature of my practice - when someone is trying to choke me out or punch me in the face, it has a remarkable tendency to bring my attention to the present instant. Funny how that works.
If these two factors don't apply to you, then your practice may be less effective at bringing you into the moment.
If you don't love your training or find it endlessly fascinating, then maybe you need a change - a different school, a different art, or even something other than martial arts.
If your training doesn't involve the sort of partner work which brings you immediate (and sometimes painful) feedback, then maybe you need a different sort of training. Alternatively, if your training is more solo work (kata, kicking air, punching bags, etc), then you may need to learn a deep internal focus that gives you continual feedback from each move you execute. (That kind of focus took me a while to develop.)
If you are doing partner training where you are getting hit or thrown and you still can't keep your thoughts in the present moment, even when your wandering thoughts get you beat up - you may want to consider getting some professional help for handling the stuff that's going on in your outside life. There's no shame in this. A good counselor is just a coach working to give you tools for handling the crap that life can throw at you.
Good luck!