The compressor shutting off is the primary reason that a mini fridge will shake profusely. The compressor is the part of the refrigerator that compacts, or compresses, the refrigerant gases in the refrigerator lines. These gases cool when allowed to expand, and occur when the compressor shuts off. The compressor works much like a common air compressor you might find in a garage -- and when these compressors stop performing correctly, there's a release of energy that causes the compressor to shake.
In some cases, the fan motor that keeps the cold air circulating throughout the mini fridge may also cause it to shake. With only slight shaking, it will continue to occur over a longer period of time. This type of shaking differs from the compressor shutting off though, as the shaking isn't violent, and the entire mini fridge doesn't rattle.
Where your refrigerator is located may also have an impact on how much it shakes. A particularly noisy mini refrigerator with a vibrating fan motor and a loud compressor will be likely to shake more if placed on a smooth surface. Such surfaces include tile floors or the tops of cabinets. You may be able to keep this shaking from occurring by using self-adhesive Velcro strips on the bottom of your compact refrigerator and the floor.
The main selling point of a compact refrigerator is that it can be installed virtually anywhere. However, those that are freestanding are more likely to experience shaking than those built into a cabinet. Some mini fridges, for example, can be encased in the existing cabinetry and installed as permanent units in a kitchen. Just remember that a refrigerator's shaking varies by model and compressor size. The shaking is not likely to be a maintenance problem -- but just part of the normal working processes of the fridge.