The time-dependent interfacial adhesion between rock and fresh mortar is key for printing concrete linings in mountain tunnels. However, a scientific deficit exists in the time-dependent evolution of the interfacial adhesion, which can cause adhesion failure when printing tunnel lining. Nanoclay has the potential to increase the interfacial adhesion and eliminate the adhesion failure. Before the actual printing of tunnel linings, the time-dependent interfacial adhesion between artificial rock and fresh mortar modified by nanoclay should be understood. This paper studied the time-dependent interfacial adhesion based on fast tack tests, fast shear tests, and isothermal calorimetry tests. With the addition of nanoclay, the maximum tensile stress and the maximum shear stress increased. Compared with a reference series, the maximum interfacial tensile stress in a 0.3% nanoclay series increased by 106% (resting time 1 min) and increased by 209% (resting time 32 min). A two-stage evolution of the interfacial adhesion was found with the addition of nanoclay. In the first stage, the time-dependent interfacial adhesion increased rapidly. A 0.3% NC series showed an increase rate six times higher than that of the reference series. As the matrices aged, the increase rate slowed down and followed a linear pattern of increase, still higher than that of the reference series. The stiffening of fresh matrices resulted in the interface failure mode transition from a ductile failure to a brittle failure. The effect of nanoclay on flocculation and on accelerating the hydration contributed to the time-dependent interfacial adhesion between artificial rock and fresh mortar.