All-solid-state lithium-sulfur batteries (ASSLSBs) are a promising next-generation battery technology. They exhibit high energy density, while mitigating intrinsic problems such as polysulfide shuttling and lithium dendrite growth that are common to liquid electrolyte-based batteries. Among the various types of solid electrolytes, solid polymer electrolytes (SPE) are attractive due to their superior flexibility and high safety. In this work, cross-linkable polymers composed of pentaerythritol tetraacrylate (PETEA) and tri(ethylene glycol) divinyl ether (PEG), are incorporated into sulfur–carbon composite cathodes to serve a dual function as both a binder and electrolyte, as a so-called catholyte. The influence of key parameters, including the sulfur–carbon ratio, catholyte content, and ionic conductivity of the electrolyte within the cathode on the electrochemical performance, was investigated. Notably, the sulfur composite cathode containing 30 wt% of the PETEA-PEG copolymer catholyte achieved a high initial discharge capacity of 1236 mAh gS−1 at a C-rate of 0.1 and 80 °C.