Hydrogel electrolytes have been widely utilized in flexible supercapacitors due to their excellent flexibility and high ionic conductivity. In this study, polybutyl acrylate (PBA) emulsion microspheres are synthesized via emulsion polymerization and introduced as hydrophobic association centers into a poly(vinyl alcohol)/polyacrylamide (PVA/PAAm) double-network hydrogel electrolyte. This electrolyte not only maintains good elasticity but also significantly enhances mechanical strength, demonstrating robust fatigue resistance. By integrating this electrolyte with ammonium molybdate-doped polypyrrole electrodes, a stretchable/compressible supercapacitor is assembled. The resultant supercapacitor exhibits a remarkable specific capacitance retention of 64.5% after 1000 stretch-release cycles under 200% tensile deformation and 68.7% after 1000 compression-release cycles under 80% compression deformation. This work presents a novel approach for designing and constructing advanced hydrogel electrolytes as well as stretchable/compressible supercapacitors.