Actin networks polymerize and depolymerize to construct highly organized structures, thereby endowing the mechanical phenotypes found in a cell. It is generally believed that the amount of filamentous actin and actin network architecture determine cytoplasmic viscoelasticity of the whole cell. However, the intrinsic complexity of a cell and the presence of endogenous cellular components make it difficult to study the differential roles of distinct actin networks in regulating cell mechanics. Here, we model a cell by using giant unilamellar vesicles (GUVs) encapsulating actin filaments and networks assembled by various actin cross-linker proteins. Perturbation of these cytoskeletal vesicles using alternating current electric fields revealed that deformability depends on actin network architecture. While actin-free vesicles exhibited large electromechanical deformations, deformations of GUVs encapsulating actin filaments were significantly dampened. The suppression of electrodeformation of actin-GUVs can be similarly recapitulated by using aqueous poly(ethylene glycol) 8000 solutions at different concentrations to modulate solution viscoelasticity. Furthermore, networks cross-linked by alpha actinin resulted in decreased GUV deformability compared with actin-filament-encapsulating GUVs, and membrane-associated actin networks, through the formation of the dendritic actin cortex, greatly dampened electrodeformation of GUVs. These results highlight that the organization of actin networks regulates the mechanics of GUVs and shed insights into the origin of differential deformability of cells.