In this study, we present SeMaScore, generated using a segment-wise mapping and scoring algorithm that serves as an evaluation metric for automatic speech recognition tasks. SeMaScore leverages both the error rate and a more robust similarity score. We show that our algorithm's score generation improves upon the state-of-the-art BERTScore. Our experimental results show that SeMaScore corresponds well with expert human assessments, signal-to-noise ratio levels, and other natural language metrics. We outperform BERTScore by 41x in metric computation speed. Overall, we demonstrate that SeMaScore serves as a more dependable evaluation metric, particularly in real-world situations involving atypical speech patterns.