chop=to cut any vegetable, fruit, or food, or firewood into smaller pieces with a knife or ax.
chip= to knock off a thin slice of. Example: When he let the glass fall it chipped a bit right near the handle. If you are eating chipped potatoes with mayonnaise, you are probably in Belgium or Holland. The bowl was beautiful but there was a chip in it and it was 30% off its original price.
slice=to cut thinly. You can slice your finger, slice a carrot, slice an orange, etc. Also, we use "slice" as a noun, and say slice of pizza, slice of lemon, slice of pie, slice of salami, etc.
dice=to cut into small cubes.
shred=to cut thin slices of either food, or paper, or cloth. Example= The important documents we sent to a special person who shreds them, assuring their confidentiality. The salad was delicious, with shredded beet, carrot, apple and vinegar and oil.