To address the straggling effect in distributed edge computing, existing methods often introduce extra computation or communication costs. Recently, information recycling has emerged as an efficient solution that avoids such extra overhead. Nonetheless, the performance of the existing information recycling-assisted rate-splitting-based distributed edge computing scheme significantly hinges on the single common stream, whose rate is limited by the edge node (EN) with the worst channel quality. To this end, a multi-group information recycling scheme for rate-splitting-based distributed edge computing is proposed, where the ENs are clustered into multiple groups, each with its own common stream. In this way, the proposed scheme alleviates the communication limitation of a single common stream, thereby boosting the information recycling mechanism for promoted computation collaboration. A K-medoids-based grouping algorithm is designed for the general multi-antenna case, and a more efficient continuous partitioning-based grouping algorithm is proposed for the special case of single-antenna. Besides, a convex–concave procedure-based algorithm is developed to solve the corresponding latency optimization problem. Simulations demonstrate that the proposed scheme offers significant and robust advantages across various communication and computation conditions. In the considered scenarios, the proposed scheme can substantially reduce the processing latency by up to 51.0% compared to the conventional information recycling scheme.