DNA origami is a powerful platform for assembling gold nanoparticle constructs, an important class of nanostructure with numerous applications. Such constructs are assembled by the association of complementary DNA oligomers. These association reactions have yields of <100%, requiring the development of methods to purify the desired product. We study the performance of centrifugation as a separation approach by combining optical and hydrodynamic measurements and computations. We demonstrate that bench-top microcentrifugation is a simple and efficient method of separating the reaction products, readily achieving purities of >90%. The gold nanoparticles play a number of critical roles in our system, functioning not only as integral components of the purified products, but also as hydrodynamic separators and optical indicators of the reaction products during the purification process. We find that separation resolution is ultimately limited by the polydispersity in the mass of the gold nanoparticles and by structural distortions of DNA origami induced by the gold nanoparticles. Our study establishes a methodology for determining the design rules for nanomanufacturing DNA origami-nanoparticle constructs.