Understanding the relation between network structure and dynamical processes is of utmost importance in many fields and in recent studies, there has been growing interest in analysing the effect of partial edge damage on random walk dynamics to better understand network functionality. In this work, we consider the effect of full damage to edges (i.e., edge removal) on the movement of a random walker and present a general framework for studying the response of random walk dynamics to one-way constraints on networks. We then apply the proposed framework to examine the impact of one-way streets on random walk dynamics in 55 urban street networks around the world.