To start off, open the kitchen cabinets which are right under the soffit you are trying to remove, and empty them in case there is something inside.
Since removing soffits can create a mess, you should use a drop-cloth right over the kitchen counter and under the cabinets. In case there is any furniture that is close to the soffits and you feel that it might get damaged, move it to the other corner of the kitchen, or outside.
Look inside the cabinet to find retaining screws right on top. These screws are basically present to hold down the soffits. Remove these screws by using a screwdriver. A drill machine can also be used to loosen any screws and it’s a faster way to do things.
Ask someone to help you hold the cabinets so that they do not fall while you are working. At times, the top of the cabinet is also glued to the soffit to provide extra bonding. In that case, use a sharp knife to scrape it off.
Check the material which the soffit is made up of and use a saw accordingly. For example, a keyhole saw can be used to cut the soffit if it is made up of drywall. Try to use a flashlight for darker corners so you do not cut down any pipes or wires which the soffit is covering.
Try not to cut any wires and once you have cut the soffit apart from one side, repeat the same process for the other side.
Once the soffit is cut, grab its piece and pull it off from the ceiling.