We propose a Distributed Intrusion Detection Framework for Cloud and Edge Computing-Assisted Internet of Things (DIDF-CECAIoT). In DIDF-CECA-IoT, edge servers are utilized to deploy optimized and pruned Deep Learning (DL) models for intrusion detection to address resource constraints. This approach helps DIDF-CECA-IoT mitigate the risk of massive attacks by detecting intrusions early and raising alerts. Cloud servers can train DL models, detect intrusions on a large scale, and disseminate model parameters to edge servers dynamically. We utilize widely adopted DL models to illustrate the working mechanisms of DIDF-CECA-IoT. The performance of DIDF-CECA-IoT is evaluated using the CICIoT2023 dataset after data pre-processing and feature selection. Results in terms of accuracy, precision, recall, and F1 score under different final sparsity values demonstrate that DIDF-CECA-IoT can effectively and efficiently balance between enhancing security and ensuring timely responses to large-scale threats in CECA-IoT.