The cold sintering of nanovaterite powder via uniaxial pressing with water involves deformation processes that operate at multiple length scales. Tomography imaging performed at scales much larger than individual agglomerates show that high uniaxial compressive strains develop within compacts containing water. This enables strong densification along the loading direction for powders subjected to stress relaxation under wet conditions. By contrast, dry pressing leads to predominantly lateral motion of the agglomerates and therefore weak densification along the pressing direction. Because lower compressive strains are achieved closer to the walls of the pressing die, a small difference in relative density between the center and the edges of compact is observed. Snapshots taken during stress relaxation experiments suggest that the vaterite agglomerates form a percolating network that quickly transmits the applied external stresses throughout the powder compact. This indicates that densification under constant mechanical load likely initiates at the contact points between the vaterite agglomerates. The high stresses developed at such contact points irreversibly deforms the network of interconnected nanoparticles inside individual agglomerates, which become truncated and more closely packed within the compact. The irreversible deformation of the nanoparticle network within each agglomerate ultimately controls the densification rate of the entire compact. This implies that possible agglomerate rearrangement events occur predominantly in the initial loading stage of the pressing operation, leaving further gains in densification to the deformation of the nanoparticles inside agglomerates. Our experimental study provides important insights onto the effect of water and powder morphology on the room-temperature cold sintering of nanovaterite and may help identify novel powders amenable to this environmental-friendly manufacturing technology.