Coring a tomato after slicing it is less than ideal, since it means additional pressure on the flesh. Instead, remove the stem first.
Using a small, very sharp paring knife and a very gentle grip on the tomato, remove the tough core at each end by going in at an angle. With the knife inserted about three-fourths of an inch from the stem, turn the tomato until you've got yourself a cone you can pop right out.
Then, begin your chopping.
Tip No. 2: For a rough cut, stack 'em up.