abstract: A subset S of a metric space X is said to coarsely separate X if the complement of an R-neighborhood of S contains at least two connected components with arbitrarily large balls. We are interested in the volume growth of such separating subsets. We show that symmetric spaces of non-compact type (except the real hyperbolic plane), higher rank thick Euclidean buildings and Bourdon's hyperbolic buildings do not admit a coarse separating subset of sub-exponential growth.