Thanks in advance ..
You could say that all three mean the same thing, and just differ in degree or intensity of motion. To chop is a more violent, forceful motion that is meant to cut something into smaller parts. To cut can mean to separate into smaller parts or just to cut partially through something. To carve means to cut with finesse or artistry, so it requires greater care and attention than just a regular cut.
I hope what I wrote makes some sense!