Distributed microphone array (DMA) is a promising next-generation platform for speech interaction, where speech enhancement (SE) is still required to improve the speech quality in noisy cases. Existing SE methods usually first gather raw waveforms at a fusion center (FC) from all devices and then design a multi-microphone model, causing high bandwidth and energy costs. In this work, we propose a \emph{Compress-and-Send Network (CaSNet)} for resource-constrained DMAs, where one microphone serves as the FC and reference. Each of other devices encodes the measured raw data into a feature matrix, which is then compressed by singular value decomposition (SVD) to produce a more compact representation. The received features at the FC are aligned via cross window query with respect to the reference, followed by neural decoding to yield spatially coherent enhanced speech. Experiments on multiple datasets show that the proposed CaSNet can save the data amount with a negligible impact on the performance compared to the uncompressed case. The reproducible code is available at https://github.com/Jokejiangv/CaSNet.