In this study, we investigate the response of self-assembled cytoskeletal structures to external mechanical perturbations, focusing on filament and crosslinker mixtures in two dimensions. By applying external forces at the microscopic scale, our work, employing agent-based models and a coarse-grained thermodynamic theory, reveals that molecular motor action enables the cytoskeletal structures to robustly adapt to changes in external forcing conditions. Specifically, under the influence of external forces, self-assembled active asters transform into bundle-like structures, and active bundle assemblies elongate further in a reproducible and regular manner, demonstrating robust responses compared to passive assemblies where no regulated qualitative morphological change was observed. A minimal thermodynamic theory, using an effective temperature concept, elucidates the adaptive properties of active assemblies. Furthermore, we explore the distinct mechanical responses resulting from morphological differences, deriving a simple form to approximate active stress as a function of the mesoscopic architecture. The results highlight the association between morphological transitions from aster to bundle and changes in the nature of active stress from contractile to extensile, confirming predictions through agent-based simulations. These findings contribute to a deeper understanding of the intricate interplay between cytoskeletal morphologies and their mechanical responses under external forces.