Everyone cuts themselves. I like to tell people I cut myself once a year just to remind myself not to do that.
Advice? Slow down, develop your technique, pay attention to the task at hand, don't worry about how fast others are going. Knife work is not a competition. If you don't learn to handle a knife properly, you will continue to cut yourself. The more adept you are at handling a knife, the less you cut yourself. If you choose to do otherwise, the knife will continue to inform you that you are wrong.