Reconstructing speech envelopes from EEG signals is essential for exploring neural mechanisms underlying speech perception. Yet, EEG variability across subjects and physiological artifacts complicate accurate reconstruction. To address this problem, we introduce Subject Disentangling Neural Network (SDN-Net), which disentangles subject identity information from reconstructed speech envelopes to enhance cross-subject reconstruction accuracy. SDN-Net integrates three key components: MLA-Codec, MPN-MI, and CTA-MTDNN. The MLA-Codec, a fully convolutional neural network, decodes EEG signals into speech envelopes. The CTA-MTDNN module, a multi-scale time-delay neural network with channel and temporal attention, extracts subject identity features from EEG signals. Lastly, the MPN-MI module, a mutual information estimator with a multi-layer perceptron, supervises the removal of subject identity information from the reconstructed speech envelope. Experiments on the Auditory EEG Decoding Dataset demonstrate that SDN-Net achieves superior performance in inner- and cross-subject speech envelope reconstruction compared to recent state-of-the-art methods.