Prompting approaches have been recently explored in text style transfer, where a textual prompt is used to query a pretrained language model (PLM) to generate style-transferred texts word by word in an autoregressive manner. However, such a generation process is less controllable and early prediction errors may affect future word predictions. In this paper, we propose a prompt-based editing approach to text style transfer. Specifically, we prompt a PLM for style classification and use the classification probability to compute a style score. Then, we perform discrete search with word-level editing to maximize a comprehensive scoring function for the style-transfer task. In this way, we transform a prompt-based generation problem into a classification one, which does not suffer from the error accumulation problem and is more controllable than the autoregressive generation of sentences. In our experiments, we performed both automatic and human evaluation on three style-transfer benchmark datasets, and show that our approach largely outperforms the existing systems that have 20 times more parameters. Additional empirical analyses further demonstrate the effectiveness of our approach.