Using discontinuously rate thickening suspensions (DRTS) as a model system, we show that beads-on-a-string morphologies can arise as a result of external viscous drag acting during capillary-driven breakup of a non-Newtonian fluid. To minimize the perturbative effect of gravity, we developed a new experimental test platform in which the filament is supported in a horizontal position at the surface of an immiscible oil bath. We show that the evolution of thin DRTS filaments during the capillary thinning process is well described by a set of one-dimensional slender filament equations. The strongly rate-dependent rheology of the test fluid and the aspect ratio of the filament couple to control the thinning dynamics and lead to a simple criterion describing the localized arrest of the capillary thinning process and the subsequent formation of complex, high aspect ratio beads-on-a-string structures.