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The cytoskeleton is a collection of protein assemblies that dynamically impose spatial structure in cells and coordinate processes such as cell division and mechanical regulation. Biopolymer filaments, cross-linking proteins, and enzymatically active motor proteins collectively self-organize into various precise cytoskeletal assemblies critical for specific biological functions. An outstanding question is how the precise spatial organization arises from the component macromolecules. We develop a system to investigate simple physical mechanisms of self-organization in biological assemblies. Using a minimal set of purified proteins, we create droplets of cross-linked biopolymer filaments. Through the addition of enzymatically active motor proteins, we construct composite assemblies, evocative of cellular structures such as spindles, where the inherent anisotropy drives motor self-organization, droplet deformation, and division into two droplets. These results suggest that simple physical principles underlie self-organization in complex biological assemblies and inform bioinspired materials design., Competing Interests: The authors declare no conflict of interest.