Design of high performance materials system requires highly efficient methods for assessing microstructure–property relations of heterogeneous materials. Toward this end, a domain decomposition, affordable analysis, and subsequent stochastic reassembly approach is proposed in this paper. The approach hierarchically decomposes the statistically representative cell (representative volume element (RVE)) into computationally tractable unrepresentative ones (statistical volume element (SVE)) at the cost of introducing uncertainty into subdomain property predictions. Random property predictions at the subscale are modeled with a random field that is subsequently reassembled into a coarse representation of the RVE. The infinite dimension of microstructure is reduced by clustering SVEs into bins defined by common microstructure attributes, with each bin containing a different apparent property random field. We additionally mitigate the computational burden in this strategy by presenting an algorithm that minimizes the number of SVEs required for convergent random field characterization. In the proposed method, the RVE thus becomes a coarse representation, or mosaic, of itself. The mosaic approach maintains sufficient microstructure detail to accurately predict the macroproperty but becomes far cheaper from a computational standpoint. A nice feature of the approach is that the stochastic reassembly process naturally creates an apparent-SVE property database whose elements may be used as mosaic building blocks. This feature enables material design because SVE-apparent properties become the building blocks of new, albeit conceptual, material mosaics. Some simple examples of possible designs are shown. The approach is demonstrated on polymer nanocomposites.