Most previous studies of document-level event extraction mainly focus on building argument chains in an autoregressive way, which achieves a certain success but is inefficient in both training and inference. In contrast to the previous studies, we propose a fast and lightweight model named as PTPCG. In our model, we design a novel strategy for event argument combination together with a non-autoregressive decoding algorithm via pruned complete graphs, which are constructed under the guidance of the automatically selected pseudo triggers. Compared to the previous systems, our system achieves competitive results with 19.8% of parameters and much lower resource consumption, taking only 3.8% GPU hours for training and up to 8.5 times faster for inference. Besides, our model shows superior compatibility for the datasets with (or without) triggers and the pseudo triggers can be the supplements for annotated triggers to make further improvements. Codes are available at https://github.com/Spico197/DocEE .