You don't have to cut your zucchini, just pick up the fruit and twist, it will pop right off. Just be gentle about pulling on the plant, zucchini is tough, you aren't going to hurt your plant. Pick the fruit when it's small about 4-5 inches long for the best flavor. The large ones have a tendency to be tough, those are best when stuffed and baked.
HELLO, IT STILL IS NOT TELLING ME WHERE TO CUT IT AT? THE REASON FOR THIS QUESTION IS THAT I DON'T WANT TO HURT THE PLANT.
This will give you some tips on picking it: