Large language models (LLMs) have demonstrated promising potential in various downstream tasks, including machine translation. However, prior work on LLM-based machine translation has mainly focused on better utilizing training data, demonstrations, or pre-defined and universal knowledge to improve performance, with a lack of consideration of decision-making like human translators. In this paper, we incorporate Thinker with the Drift-Diffusion Model (Thinker-DDM) to address this issue. We then redefine the Drift-Diffusion process to emulate human translators' dynamic decision-making under constrained resources. We conduct extensive experiments under the high-resource, low-resource, and commonsense translation settings using the WMT22 and CommonMT datasets, in which Thinker-DDM outperforms baselines in the first two scenarios. We also perform additional analysis and evaluation on commonsense translation to illustrate the high effectiveness and efficacy of the proposed method.