This paper focuses on severe variable missingness and variable sparsity in device-edge collaboration. Inference-based methods yield unacceptable reconstruction errors under high missing rates, thus necessitating retransmission. However, this approach can lead to network congestion and even break-down in emergency response scenarios. To overcome these limitations, we propose a Similarity-based Multivariate Data Completion Framework (SMDCF). Unlike traditional retransmission approaches, SMDCF adopts an innovative similarity-based learning paradigm. For handling variable missingness, the framework retrieves similar samples from offline datasets by analyzing sparse observations and then effectively transfers relevant variables from these reference samples to complement the incomplete data; for handling variable sparsity, SMDCF employs graph neural networks to systematically model three key relationships: inter-sample correlations, inter-variable dependencies, and intra-variable patterns, thereby achieving robust and reliable missing-value inference. Comprehensive experimental results demonstrate that SMDCF consistently delivers superior performance under various data missing scenarios. Notably, even under an extreme 90% missing data rate, our framework reduces the reconstruction error by 8.37%.