Anomalous transport in fractured rocks is of high importance for numerous research fields and applications in hydrogeology and has been widely studied in the last decades. This phenomenon is due to the structural heterogeneities of fractured rocks and the high contrast between the fractures and matrix properties. At the same time, the fracture properties in terms of fracture density and geometrical characteristics are related to in-situ stress conditions that impact the connectivity of the system and the distributions of fracture aperture and length, including the creation of new cracks when the differential stress conditions are strong enough. In order to understand how all these features impact the observed anomalous transport, we study the role of in-situ stress in mass transport through a two-dimensional fractured rock. The fracture network is based on a real outcrop with a connectivity state around the percolation threshold, over which we simulate stress-dependent fracture deformation and propagation, and perform hydrodynamic transport through the deformed rock mass. The impact of the changes in aperture and the creation of new cracks on transport behavior is evaluated for various stress scenarios and reproduced with upscaled representations of transport processes. We also consider matrix diffusion as a source of anomalous transport and demonstrate that this process can be incorporated into the proposed upscaled models. Results showed that traditional upscaling methods with space-Lagrangian velocities description capture well the Gaussian-like breakthrough curves (BTCs) under low-stress ratio conditions, but fail under high-stress ratio conditions with multiple-peak early-times BTCs. To characterize the emergence of strong anomalous transport, we extend the Random Walk model Directed by a Markov Process with space-Lagrangian velocity sampling by incorporating multiple transition matrices conditioned by different initial velocity states. This new transport upscaling model shows high accuracy in predicting complex transport behaviors in critically connected fracture networks.