Is carbon lost from topsoil when it's degraded/removed? What is the scientific process?
There are two ways carbon is released from soil.
The first is cellular respiration of plants that uses previously stored energy (visualized in this chart).
The second is when heterotrophs consume organic carbon below ground and respire carbon dioxide.
The sum of these is called soil respiration, which I think was the process you were asking about.
Soil loses net carbon when disturbance stops carbon fixation but does not stop carbon respiration.
Carbon is fixed into organic material by photosynthesis, mostly by plants; carbon respiration is when organic material rots or is eaten, as described by communitys. Undisturbed soils have fluxes of carbon both in and out almost all the time.
Most human disturbances reduce photosynthesis, so "disturbed soils release carbon" is an adequate shorthand. For instance, plow agriculture that keeps soil bare of plants for a significant part of the year; or moving piles of soil around for construction, or diverting streams and groundwater so that plants die of drought, or simply paving over soil. Natural disturbances can do the same.
As ecosystems mature on undisturbed soil, they tend to become more efficient at capturing energy and retaining limiting nutrients and therefore gain biomass, including soil organic material (SOM). SOM not only literally contains nutrients, but is a micro-environment that buffers nutrients, buffers water, and supports microbes that help plant roots flourish, which is why agriculture benefits from increased SOM.
Even in wild environments, leaching eventually reduces the soluble nutrients and reduces total biomass (see Vitousek & Reiners, 1975, and a lot of Vitousek's later work). The leaching takes long enough that it's also an adequate shorthand to say that undisturbed soils will accumulate soil carbon.