I have a soffit over my cabinets, can I cut only it out?

One of the purposes of a soffit is to conceal duct work, plumbing and electrical lines that run through the kitchen. In fact, many of the first soffits were built for this reason: as a way of boxing in mechanical and electrical items that would otherwise have nowhere to go. If you choose to remove your soffit, cut a hole in the side and look in there first. If it's empty, there is little difficulty in removing it. If it is full of pipes or duct work, the difficulty lies in rerouting these items. This means either opening the ceiling or the wall behind them to give them a place to go.

If you do not have the blueprints to your home, proceed with caution. Sometimes they are empty dead space, other times they run ducting, electrical or plumbing through the soffit space. You won't know until you open it up. Cut a small hole in several locations and take a look. If empty, have at it. If there are utilities running through, they will need to be rerouted (this is where costs rise significantly and you need to pull a permit - check local building codes), before you can get rid of them.

txhed pa May be hiding HVAC duct or plumbing pipes. Knock a small hole in they drywall and take a look. If nothing is being run through it then you are free to take down. If duct work or plumbing pipes etc those would have to be reworked and could get very expensive depending on what you find. Small hole can be patched easily if you do not end up removing all together.

In order to be able to raise the fridge up to accommodate the increased thickness in the floor, instead of cutting into the soffit, why not just remove the small upper cabinet? ( I am assuming that those cereal boxes are on the top of the fridge.)This would give more 'headroom' to raise the fridge up.

From the picture, it does not look like that cabinet is providing you with very useful storage space anyway. Take it off, and remount it somewhere else in the home where it can be put to more efficient use.

Where my soffit sits, there is no room to store items as it’s just under the roof line to keep the cabinets in line with the others as they turn a corner.

To make it easy to move the fridge around, get some furniture/appliance moving sliders first. They are sold under different brand names, come in different sizes and shapes, but all do the job. They protect your floor, and help save your back. Super Sliders is one commonly available brand.