Here we evaluate the performance of bump arrays to separate large particles from non-Newtonian slurries with Bingham and Cross rheology. Bump arrays in deterministic lateral displacement devices separate large particles from small particles using arrays of staggered posts. Large particles, defined as those with radii larger than the distance between the edge of a post and the stagnation streamline from the next downstream post, must bump toward one side of the device, whereas particles smaller than this distance slalom from entrance to exit without net lateral displacement. Although these devices have been used to separate a wide variety of large particles from blood cells to sand, partition of large particles from non-Newtonian fluids remains unexplored. Yet, an important set of modestly concentrated slurries, including Hanford nuclear waste, displays non-Newtonian rheology. Here we evaluate the influence of non-Newtonian rheology on the large-small particle size cutoff in bump arrays using a model that explores the influence of yield stresses, ratios of zero and infinite shear viscosities, and Cross’s exponent under strictly laminar well-developed conditions. Surprisingly, we find that viscosity ratios and Cross’s exponent make no significant difference on the particle cutoffs between large particles that bump and small particles that slalom around the posts from entrance to exit. In contrast, we find that yield stresses do significantly affect the size cutoff. As the yield stress increases, velocity profiles become more plug like lowering the size cutoff. For nuclear waste separations where removing large particles is a priority, increasing yield stresses is conservative.