First thing – have and keep your knives sharp. That allows them to do more of the work. You do not need a death grip on your knives if they are doing the work.
When slicing round stuff, cut them in half first and put the cut side down before slicing. The stable base makes accidents less likely.
Use a slicing motion when cutting. It is much easier than trying to chop through your victim, vegetable.
Now that you have gotten your knives sharpened you want to keep them sharp. Hone them after each use and store them sharp side up in your knife block.
Do not store your knives willy nilly in a drawer. It dulls the blades and makes you more likely to get cut reaching for one. If you have a knife “block” in your drawer, make sure you cover the blade portion so you don’t get cut reaching for one like I did. Duh.
When scraping your beautifully diced food off your board to make your honey a wonderful Valentine’s day dinner turn the knife upside down so you don’t dull your blade or scrape off some of the board with your food.
Wash and hone your knife after each use, so it is ready to go at a moments notice.