This paper divides the problem-solving process into six main stages: problem identification, information gathering, analysis, comprehension and judgment, solution derivation, and problem resolution. It then conducts an in-depth analysis of the corresponding sign language expressions in Korean Sign Language (KSL). Through this systematic approach, the study aims to elucidate the cognitive mechanisms underlying sign language expressions in the context of problem-solving in KSL and to explain the relationship between the forms of sign language and their abstract meanings. The investigation reveals several key characteristics. First, ontological metaphors, which conceptualize abstract concepts as concrete objects, are most frequently employed in the metaphorical mappings of sign language. Second, the sign language expressions related to problem-solving are predominantly action-based iconic signs. Third, conceptual metonymy and metaphor are the primary cognitive mechanisms for constructing the abstract meanings of these expressions. Additionally, like spoken language, sign language involves complex cognitive processes. These include metonymy, metaphor combined with metonymy, multiple interacting metaphors, multiple metonymies combined with a metaphor, metonymy combined with multiple metaphors, and other intricate combinations.