Split learning (SL) transfers most of the training workload to the server, which alleviates computational burden on client devices. However, the transmission of intermediate feature representations, referred to as smashed data, incurs significant communication overhead, particularly when a large number of client devices are involved. To address this challenge, we propose an adaptive channel pruning-aided SL (ACP-SL) scheme. In ACP-SL, a label-aware channel importance scoring (LCIS) module is designed to generate channel importance scores, distinguishing important channels from less important ones. Based on these scores, an adaptive channel pruning (ACP) module is developed to prune less important channels, thereby compressing the corresponding smashed data and reducing the communication overhead. Experimental results show that ACP-SL consistently outperforms benchmark schemes in test accuracy. Furthermore, it reaches a target test accuracy in fewer training rounds, thereby reducing communication overhead.