Open the kitchen cabinets beneath the soffit that you are removing. Remove anything that may be stored inside such as dishes or food items.
Place a dropcloth over the kitchen counter beneath the cabinets. Removing soffits can be quite messy. Move any furniture that you don't want damaged to another part of the kitchen or another room.
Look inside the cabinets for the retaining screws holding them in place to the kitchen wall. There may also be screws attaching the top of the cabinet to the underside of the soffit. Remove these by unscrewing them with a screwdriver or power drill and screwdriver attachment. Have an assistant hold the cabinets in place while you are working so they don't suddenly fall out of place. You may need to use a sharp utility knife to cut apart the top of the cabinet from any caulk or glue connecting it to the soffit.
Examine the soffits from underneath to determine their material and placement. This will help you determine the best tool to saw the soffits apart. If they are made of drywall, for example, you can use a keyhole saw to cut the soffits apart. Harder materials, such as wood, will require a jigsaw or other powered saw. Use a flashlight to help light up any dark corners. While you are looking, make a note of any pipes or wiring that the soffits may be concealing.
Start at the corners by sawing the soffits apart with the appropriate tool. Steer clear of any pipes or wires while cutting to avoid accidents. Once the corner is cut, repeat the process on the opposite side of the soffit.
Grab the soffit piece and pull it out away from the wall or ceiling. Repeat this process for all of the portions of Soffit as needed.