You may want to try your question on other more mechanically oriented forums. This one is heavily electronics oriented.
While I don't have experience on your particular model, I have worked on similar equipment as a DIYer. I would say the ability for you to repair this will depend heavily on your skills. If you have a reasonable set of small tools and have worked on automobile engines and/or kitchen appliances you can probably pull this repair off. Be guided by your past experience. If you have taken a lot of things apart and put them back together you will be fine. If you have taken a lot of things apart, but not gotten them all back together be more cautious. If you have only watched YouTube videos be very cautious.
First, remember safety. Take power off of the machine. Then remove covers to get to the actual punch mechanism. You should be able to see both the punches and the punch plate. Make sure you look over the mechanism and understand any spring preloads which could be released when your fingers are in an unfortunate position. You can take a small probe and make sure that all of the holes in the punch plate are clear, paying particular attention to the problem holes. I have used a small drill bit to help clear these holes, just be sure not to ding or damage the holes themselves. If wedged in paper is the problem it will be very firmly wedged to resist a force capable of punching through several dozen sheets of paper. You will probably not be able to just force it on through, but will have to worm a few pieces at a time out. Dental picks can also be useful. Be sure to check the waste chute and/or bin which collects the punchings. The holes may have jammed because the chutes or bin were clogged or full.
While you are inside the machine you probably should check for dirt and debris in the punch side of the mechanism which might reduce punching force and if you aren't paying for maintenance on this machine check for obvious lubrication points and make sure that they are appropriately lubed.
A lot will depend on whether this machine is mission critical for you job or business. If it is, think about whether your time is better spent figuring out how to get a pro in to work on it.
Best of luck and have fun if you decide to tackle this.