Glaciers across High Mountain Asia (HMA) are thinning and retreating in widely varying patterns. The cause of this variability has been controversial for decades, hindering predictions of water resources and hazards for 800 million people downstream. We show that this heterogeneity is strongly affected by debris cover on glaciers. We propose a new mechanism: that debris cover, by reducing surface melt rates and glacier slopes, limits the dynamic propagation of thinning to glacier termini. The resulting patterns of thinning lead to new supraglacial and ice marginal lakes, which are capable of draining catastrophically. Explanation of this new physical mechanism for thinning allows prediction of emerging hazards in HMA in the face of rising temperature and a diminishing cryosphere.