Fetal electrocardiogram (FECG) morphology plays an essential role in the early diagnosis of fetal health conditions. However, it is intractable to extract the clean morphology of FECG signals, which are usually contaminated by maternal ECG (MECG) and various noises. To extract the clean morphology of FECG signals from non-invasive abdominal ECG records, a high-performance and high-efficient two-stage slow-fast long short-term memory (SFLSTM) based architecture is proposed. The MECG elimination and the FECG enhancement are realized by the elaborately designed slow LSTM and fast LSTM to filter out the MECG and the residual noise components. Qualitative and quantitative experiments are conducted on the records from two public datasets. The experimental results reveal that our designed scheme achieves the best performance in kSQI, signal-to-noise ratio (SNR), and root mean square error (RMSE). The MECG elimination and the FECG enhancement improve SNR by 3.09 and 1.81 dB, respectively. The proposed fast LSTM reduces computation cost by approximately 50%, without any degradation in performance. Our method may leverage non-invasive FECG monitoring for the early detection of fetal heart diseases.