Space-based gravitational wave (GW) detectors will be able to observe signals from sources that are otherwise nearly impossible from current ground-based detection. Consequently, the well established signal detection method, matched filtering, will require a complex template bank, leading to a computational cost that is too expensive in practice. Here, we develop a high-accuracy GW signal detection and extraction method for all space-based GW sources. As a proof of concept, we show that a science-driven and uniform multi-stage deep neural network can identify synthetic signals that are submerged in Gaussian noise. Our method has more than 99% accuracy for signal detection of various sources while obtaining at least 95% similarity compared with target signals. We further demonstrate the interpretability and strong generalization behavior for several extended scenarios.