Locate a good work surface where you can cut the box. If working with a big box, your driveway or front yard may work best.
Fill the box with the items you want in it and use a permanent marker to indicate on the outside of the box, the height of the box when full. Do this on all four corners.
Empty the box and deconstruct it so that it's flat. This may require removing tape or pulling the bottom pieces apart if they are just folded together. Working with a flat box is much easier and safer than with an open one.
Lay the box on your work surface. Using your utility knife, cut down each corner, following the seam, from the top to the mark you made with your permanent marker. This will be the new depth for your box. Do this for two corners.
Flip the box over and repeat the cut above at the remaining two corners, ensuring that you cut from the top down, following the seam, to your permanent mark.
Pick up your ruler and measure the depth of the cut you made on each corner. This will be the amount of box top that you will trim from both the length and width of the box to ensure it closes properly.
Grasp the box, with it lying lengthwise, putting a hand on either side at the bottom of your fresh cut. Now bend it by pulling towards you. If it gives you trouble, put your ruler underneath the fold line so that it folds evenly.
Release the flap and grab your ruler with one hand and your marker with the other. Using your earlier measurement, lay your ruler vertically on the flap starting at the outermost edge and measure down it, marking the place where you'll cut.
Lay your ruler horizontally across the top of the flap, aligning it with each mark. Using the ruler as a guide, cut deeply into the cardboard to get both flaps and go all away across the top. This will trim any excess carboard across the lengthwise portion of your box.
Measure down the side of each end flap while they're flat and repeat the above steps, laying the ruler across and cutting each end flap.
Stand the box up and assemble the bottom piece. Flip it so that the end pieces that haven't been bent, are facing you. Grasping the flap on either side where the fresh cut was made, bend the box toward you. You are now ready to fill your new smaller box.