When the punch contacts the material, it will draw some of the material inward as it shears and penetrates. Minimizing sheet distortion boils down to mitigating this effect.
First, make sure the die clearance accounts for this material draw. If you have too little clearance, you are prevented from having the material fracturing cleanly. This can result in galling and can distort the surrounding material.
Provide clamping pressure before punching when you start as it will help in not just with forming on the punch press, but actual punching as well. You may choose to use a smaller stripper plate or have a smaller surface area on the die. This might reduce the overall pressure required to punch the material, but because you’re working over a smaller area, the pounds of pressure per square inch goes up. This in turn can help reduce the chance for the sheet to distort.
Please note that this pressure can increase sheet marking, especially in soft aluminum and other similar material. You are, after all, increasing pressure on the flat sheet, and some sheet metal grades are sensitive to this. Regardless, for most materials the marking usually is very minor, if it’s noticeable at all.
If you have a lot of holes to punch in a small area and you can't increase the spacing between the holes, you may try programming the machine to punch the holes randomly, rather than going back and forth in a linear pattern.
Another way to minimize sheet distortion is hole shaving. When hole shaving, the machine uses the same die size but two different punch sizes for the same hole. It punches first with the smaller punch (say, 9.8 mm in diameter) and then follows it with a second larger punch (like with a 10-mm-diameter tool). This larger second punch “shaves off” the stressed area surrounding the hole perimeter.