As a typical sequence to sequence task, sign language production (SLP) aims to automatically translate spoken language sentences into the corresponding sign language sequences. The existing SLP methods can be classified into two categories: autoregressive and non-autoregressive SLP. The autoregressive methods suffer from high latency and error accumulation caused by the long-term dependence between current output and the previous poses. And non-autoregressive methods suffer from repetition and omission during the parallel decoding process. To remedy these issues in SLP, we propose a novel method named Pyramid Semi-Autoregressive Transformer with Rich Semantics (PSAT-RS) in this paper. In PSAT-RS, we first introduce a pyramid Semi-Autoregressive mechanism with dividing target sequence into groups in a coarse-to-fine manner, which globally keeps the autoregressive property while locally generating target frames. Meanwhile, the relaxed masked attention mechanism is adopted to make the decoder not only capture the pose sequences in the previous groups, but also pay attention to the current group. Finally, considering the importance of spatial-temporal information, we also design a Rich Semantics embedding (RS) module to encode the sequential information both on time dimension and spatial displacement into the same high-dimensional space. This significantly improves the coordination of joints motion, making the generated sign language videos more natural. Results of our experiments conducted on RWTH-PHOENIX-Weather-2014T and CSL datasets show that the proposed PSAT-RS is competitive to the state-of-the-art autoregressive and non-autoregressive SLP models, achieving a better trade-off between speed and accuracy.