Efficient and accurate analysis of materials behavior across multiple scales is critically important in designing complex materials systems with exceptional performance. For heterogeneous materials, apparent properties are typically computed by averaging stress-strain behavior in a statistically representative cell. To be statistically representative, such cells must be larger and are often computationally intractable, especially with standard computing resources. In this research, a stochastic reassembly approach is proposed for managing the information complexity and reducing the computational burden, while maintaining accuracy, of apparent property prediction of heterogeneous materials. The approach relies on a hierarchical decomposition strategy that carries the materials analyses at two levels, the RVE (representative volume element) level and the SVE (statistical volume element) level. The hierarchical decomposition process uses clustering methods to group SVEs with similar microstructure features. The stochastic reassembly process then uses ttesting to minimize the number of SVEs to garner their own apparent properties and fits a random field model to high-dimensional properties to be put back into the RVE. The RVE thus becomes a coarse representation, or "mosaic," of itself. Such a mosaic approach maintains sufficient microstructure detail to accurately predict the macro-property 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. Thus, material design studies may be undertaken with SVE- Apparent properties as the building blocks of a new material's mosaic. Some simple examples of possible designs are shown. The approach is demonstrated on polymer nanocomposites.