Landscapes respond to climate, tectonic motions and sea level, but this response is mediated by sediment transport. Understanding transmission of environmental signals is crucial for predicting landscape response to climate change, and interpreting paleo-climate and tectonics from stratigraphy. Here we propose that sediment transport can act as a nonlinear filter that completely destroys ("shreds") environmental signals. This results from ubiquitous thresholds in sediment transport systems; e.g., landsliding, bed load transport, and river avulsion. This "morphodynamic turbulence" is analogous to turbulence in fluid flows, where energy injected at one frequency is smeared across a range of scales. We show with a numerical model that external signals are shredded when their time and amplitude scales fall within the ranges of morphodynamic turbulence. As signal frequency increases, signal preservation becomes the exception rather than the rule, suggesting a critical re-examination of purported sedimentary signals of external forcing.