In this paper, we propose an effective yet efficient model PAIE for both sentence-level and document-level Event Argument Extraction (EAE), which also generalizes well when there is a lack of training data. On the one hand, PAIE utilizes prompt tuning for extractive objectives to take the best advantages of Pre-trained Language Models (PLMs). It introduces two span selectors based on the prompt to select start/end tokens among input texts for each role. On the other hand, it captures argument interactions via multi-role prompts and conducts joint optimization with optimal span assignments via a bipartite matching loss. Also, with a flexible prompt design, PAIE can extract multiple arguments with the same role instead of conventional heuristic threshold tuning. We have conducted extensive experiments on three benchmarks, including both sentence- and document-level EAE. The results present promising improvements from PAIE (3.5% and 2.3% F1 gains in average on three benchmarks, for PAIE-base and PAIE-large respectively). Further analysis demonstrates the efficiency, generalization to few-shot settings, and effectiveness of different extractive prompt tuning strategies. Our code is available at https://github.com/mayubo2333/PAIE.